maximum of two exponential random variables

Problem 17. Add to FlexBook Textbook. Game development in computers relies heavily on trigonometry. Q1: What is trigonometry and its applications?Ans: Trigonometry has got a lot of applications in different areas of life including Engineering, Arts, Music, Games, etc. For example, using radar which shows the distance tothe plane, the controller can work out the right angle of descent that the pilot should take using trigonometry principles. In simple terms, Trigonometry means calculations with triangles. =\frac{1+1-4}{4}\\ Necessary cookies are absolutely essential for the website to function properly. Once an airplane is up in the sky, it is not the engine or the pilots skill that keeps it floating. "text": "Hipparchus is considered the father of trigonometry." To accurately reach your location, you need to account for wind speed or you risk going off course. In construction we need trigonometry to calculate the following: Architects use trigonometry to calculate structural load, roof slopes, ground surfaces, and many other aspects, including sun shading and light angles. google_ad_client: "ca-pub-5871853733714179", In marine engineering, trigonometry is used to build and navigate marine vessels. Originating in ancient Greece, trigonometry is an amalgamation of two words, trigono meaning triangle, and metry meaning measure. Trigonometry Worksheets Grade 10 Cbse trigonometri-logaritma.blogspot.com. Throughout history, astronomers have used trigonometry to calculate the distances of stars and planets from Earth. We already told you about aviation and space. SQL and List Of Speech Sound Examples And Resources, 18 Famous Quotes Involving The Concept Of Fractions, 7 Engaging Games For Learning Rational And Irrational Numbers. The height of the building, the width length, etc., and the many other such things where it becomes necessary to use trigonometry. "@type": "Answer", This transformation popularized the applications of trigonometry by demonstrating that a mathematical representation of natural occurrences is feasible. When you see an excavation site, you will see that the area is not dug up randomly. GPS, or Global Positioning System, uses triangular trigonometric techniques while orbiting over specific locations on earth. According to Morris Kline, in his book named Mathematical Thought from Ancient to Modern Times, proclaimed trigonometry was first developed in connection with astronomy, with applications to navigation and construction of calendars. What are the reasons to buy Twitch viewers? (i) Marine Engineering You can find the answer by connecting the algaes position, depth of the algae from the sea surface, and angle of sunlight. View 56. Trigonometry helps Mario jump over these obstacles. It is also used to see the horizon. ", Solution to Problem 1: Use the tangent tan (18 o) = h / 100 Solve for h to obtain h = 100 tan (18 o) = 32.5 meters. For that, please check our blog on the trigonometry table. The Astounding Brilliance and Greatest Contributions of John von Neumann. = 5/13 0.3846 cos S = adj./hyp. If the angle of elevation to . However, in the real world all objects are three dimensional, so it is important that we extend the application of the area, sine and cosine formulae to three dimensional situations. The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects.1, Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.- Sir Isaac Newton.1 When you hear the, Math can be broadly divided into three major branches: arithmetic, algebra, and geometry. Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings, etc. This cookie is set by GDPR Cookie Consent plugin. one example in carpentry is making 45 degree angles onto molds so it can turn corners. So, whatever there is to manufacture from scratch, trigonometry has extended helping hands. This can be in four forms: maritime, aviation, terrestrial, and space. trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. So, the triangle measurement is the sum of its sides and angles. See more ideas about trigonometry, the real world, real. Likewise, the diagnosis and treatment of illnesses using a variety of imaging, ultrasound, nuclear medicine, and magnetic resonance techniques are uses of trigonometry. Example 1: If it takes 40 seconds to run around a circular 100 meter track, They can be so widely used in real life applications and is very I can conclude that without trigonometry, life would be I just modified your conclusion to. When flying a plane, you need to constantly know its speed and direction and how this interacts with wind speed. Example(1): Express the eight points of the compass shown in the diagram as bearings from north. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). } Sine, Cosine, Tangent Real World Applications. . Marine biologists often use trigonometry formula to establish measurements. -To make roof of a house inclined the engineers use trigonometry Real-life applications of Trigonometry have helped in the development of everyday human life activities. The cookie is used to store the user consent for the cookies in the category "Analytics". With the value of the right angle known, they can easily decide the height of the dress. tan = 150/ 150 3. tan = 1/ 3. = 3 0 Example 3 : Suppose two insects A and B can hear each other up to a range of 2 m. Java, 2. The Father of Math - Want to know who created Math? Copyright 2022 . "@type": "FAQPage", PowToon is a free. Two perpendicular sides of a right-angled triangle depict the winds direction. Their names and acronyms are: The fundamental notions of trigonometry are the angle functions and their applications to computations. Solve for the vertical heights ( b and a) in the two separate triangles. It is also used to find the distance of the shore from a point in the ocean. The larger of them is 3 times larger than the smaller. Yes, you got it right. For this, they often use trigonometry. The control and monitorization of moving vehicles are explored in various forms of navigation. What is the maximum and minimum problems in DAA? They study the sound waves created by sine and cosine curves, analyze and comprehend the music and make necessary changes. After our Real World Math Trigonometry Lesson, I will be able to: analyse a real-world situation and make a connection to the prior knowledge I have learned throughout this math course, deconstruct the problem and use prior knowledge of the primary trigonometric ratios acquired throughout this unit to create a solution to the problem, Of each group will compare with the only max of another group and min with min. Using trigonometry principles, your receiver can calculate its exact position using the satellites. 2. As you know Gaming industry is all about IT and computers and hence Trigonometry is of equal importance for these engineers. Python, C, "name": "What is trigonometry and its applications? Trigonometry basics deal with the measurement of angles and problems related to angles. If the sin of angle A is 0.3, find cos of angle A? Evaluate each of the following integrals. 4 quadrants as well as examples of trig ratios in all 4 quadrants. They also make use of computer-aided design tools that incorporate principles of trigonometry 2. It is used in navigation to pinpoint a location. In every game, there are objects that move. trigonometry intuitively. Problem 16. So, we can compute the planes distance to its destination by applying the definition of trigonometric ratios. The study of moving objects is known as navigation, and the angle or distance measured at that time is done with trigonometry. 9 Fun Geoboard Games And Apps For Little Learners, 8 Fun Day And Night Activities For Preschoolers, 5 Fun Interview Activity Ideas For High School Students, 20 Helpful Examples Of Descriptive & Evaluative Feedbacks For Students, NumberDyslexia is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com. 1. They can also use it to measure the distance from underground water systems. We regularly post articles on the topic to assist students and adults struggling with their day to day lives due to these learning disabilities. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. Some . "@context": "https://schema.org", This cookie is set by GDPR Cookie Consent plugin. 2. All involve right triangle trig (SOH CAH TOA) Dislike Share MrStanislow 3.17K. The job mandatory basic of high school math. Math for Real Life College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical Page 1/9 Let T (n) = time required to apply the algorithm on an array of size n. Here we divide the . Solution: If the smaller number is x then the big number is 3x. =4. Download. New IITs Vs BITS Pilani, which is better and why? Answer: Vibrations and oscillations are often described or approximated by a combination of harmonic functions, even when these oscillations are not mono-harmonic. An architects blueprint includes many trigonometric elements where their findings are compared for implementation into the plan. Air Traffic Control uses the speed and angle of flying of the airplane and the speed of the wind. "@type": "Answer", R Solution (a) : The length of the hypotenuse is 13. Calculate the exact value of sin15. An example of data being processed may be a unique identifier stored in a cookie. Engineers in the automobile industry manufacture vehicles with utmost perfection by accurately calculating trigonometric formulas to estimate the size of the items. can be determined by using knowledge of trigonometry. Its top and the open end of the shadow form the hypotenuse allowing you to visualize the right triangle structure. -In fact, calculus uses trigonometry and algebra Example for: opposite = tan x adjacent Put the given values (hypotenuse and angle) into the formula: tan = o a tan 43o = b 16 Rearrange the formula to make the unknown (opposite)the subject (on the left . "name": "What are 6 occupations that use trigonometry? Problem 1: Prove \sin^2 \frac{\pi}{6} +\cos^2\frac{\pi}{3}-\tan^2\frac{\pi}{4}=-\frac{1}{2}, Solution: We have, Engineers use trigonometric relationships to predict the sizes and angles of mechanical parts used in machinery, tools, and equipment. Trigonometry Applications in Real Life. Precipitation Reaction Examples in Real Life. Modern trigonometry is heavily influenced by Babylonian, Sumerian, Greek, and Indian astronomers. Estimate the height h of the tree to the nearest tenth of a meter. All rights reserved. Errors made by students with Circular Functions<br />1. = 5/12 0.4167 Solution (b) : Trigonometry will help to solve for that third side of your triangle which will lead the plane in the right direction, the plane will actually travel with the force of wind added on to its course. Archaeologists identify different tools used by the civilisation, and using trigonometry can help them in these excavates. Now use it as an example of a unit circle. Modern trigonometry evolved during the Western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and culminating with Leonhard Euler (1748). Yes, they use trigonometry to calculate how far a planet or a star is from Earth. Every time any exam result is out, we witness toppers making it big, with some students obtaining a perfect score -- acing the test while others nearly nailing it. Archaeologists label and mark rock layers into numbered plots to identify which artifact was in which province, calculate the underground position of an artifact from above the ground using their position as the observation point and angle between the artifact and observation point surface, etc. So during carpentry work angles are made all the time to make sure the material and other equipment can fit exactly in the space that is available. PHP, sin42.5 = x 300 300 sin42.5 = x x 202.7 The kite is about 202.7 feet off of the ground. Android, There are many geometric forms all around you, and squares are among the most prevalent. you should draw and label a picture of this word problem. Play a game of building an imaginary tree house. "@type": "Answer", ", These functions can help you work out the unknown lengths of a triangle if you know the angle and one of its lengths. Architecture Architects use trigonometry to design buildings. You may use want to use some mnemonics to help you remember the trigonometric functions. Even in projectile motion, you have a lot of application of trigonometry. Let the top of the rope attached to the top of the tree be point A. 2 cos3(1 2 w)sin5( 1 2w) dw 2 cos 3 ( 1 2 w . A boy is standing near a tree. A climbing ladder leaning to the wall: A . Marine biology, or the study of plants and animals inhabiting the ocean, also uses trigonometry. A right-angled triangle has three sides with the hypotenuse being its longest side. Applications of Sine, Cosine, Tangent in Real World SOHCAHTOA ratios Sine, Cosine, Tangent to Solve for Side of Right Triangle Sine Cosine Calculator Then let B be the base of the tree. While a plane is flying, the wind plays an integral part in integrating safety and technology. Trigonometry was a significant topic of study in Islamic mathematics during the Middle Ages, as demonstrated by mathematicians such as Al-Khwarizmi and Abu al-Wafa. "@type": "Question", Right Triangle Trigonometry: Real Life Problems By Dr Pepper Lover www . Calculus is made up of Trigonometry and Algebra. }); In simple terms, trigonometry is the ratio of lengths, angles, and triangles. A rectangle is a four-sided shape whose corners are all ninety-degree angles. Calculating them with the tan function will give you the height. Add to Library. Problems in three dimensions (EMCGN) Trigonometric formulae are useful for solving problems in two dimensions. Notes/Highlights. 11,943 views Nov 9, 2012 7 examples of trigonometric problems that you may encounter in real life. Trigonometry is a study of the relation between the sides of the angles of a triangle. Step 3: Using the. These give the following vital functions: We get these by dividing one side with another in a right-angled triangle. To learn the trigonometry concept, contact our Maths expert and become a trigonometry expert today. "acceptedAnswer": { Step 1: Set your given trigonometric function equal to the given constant value. Q2: What are 6 occupations that use trigonometry?Ans: Six occupations that use trigonometry are:(i) Marine Engineering(ii) Game Development(iii) Construction(iv) Naval & Aviation(vi) Criminology. Trigonometry in physics: Trigonometry is the branch of mathematics that studies triangles and their relationships. The primary application of trigonometry is found in scientific studies where precise distances need to be measured. }] Maximum board toppers took admission in BITS-Pilani for higher studies, JEE Advanced attempts A candidate can appear in two consecutive years. Made with <3 creative team @ 2021 Letstacle.com, Terms of Use | Disclaimer | Privacy Policy, \sin^2 \frac{\pi}{6} +\cos^2\frac{\pi}{3}-\tan^2\frac{\pi}{4}=-\frac{1}{2}, LHS=\sin^2 \frac{\pi}{6} +\cos^2\frac{\pi}{3}-\tan^2\frac{\pi}{4}=(\frac{1}{2})^2+(\frac{1}{2})^2-(1)^2\\, \sin (45-30)= \sin 45 \cos 30- \cos 45 \sin 30 (Using trigonometry formula i.e \sin(a-b) = \sin(a)\cos(b)\cos(a)\sin(b)) \\, =(\frac{1}{\surd 2})(\frac{\surd 3}{2})-(\frac{1}{\surd 2})(\frac{1}{2})\\, \tan 15 = \frac{\tan 45 - \tan 30}{1+\tan 45 \tan 30 }=\frac{\surd 3-1}{\surd 3+1}\\, \cot 15=\frac{1}{\tan 15}=\frac{\surd 3+1}{\surd 3-1}\\, \therefore \tan 15 +cot 15 =\frac{\surd 3-1}{\surd 3+1}+\frac{\surd 3+1}{\surd 3-1}\\, =\frac{(\surd 3-1)^2+(\surd 3+1)^2}{(\surd 3+1)(\surd 3-1)}\\, Library System: Business Rules and User Requirements, Programming Project 5: lo shu Magic Square c++, 7 Laptop for Python Programming Suggestions for New Coders, Top 5 Online Tools for Base64 Encoding and Decoding. Neil Armstrong and Edwin Aldrin successfully etched their name in history by landing on the moon only because trigonometry helped in all the calculations. In simple terms, if we know the two sides of a right-angle triangle then thirds sided can be calculated using the Pythagoras theorem. A few more examples of where trigonometry techniques are widely applied are optics, statistics, electrical engineering, mechanical engineering, computer graphics, game development, civil engineering, cartography (creating maps), and crystallography (the study of atom arrangements in a crystalline solid).At BYJUS FutureSchool, students are offered an extensive curriculum to help master the concepts of trigonometry and overcome math anxiety. Case 1: Special angle 45o (from a 45o - 45o - 90o triangle) The following figure 7-1 represents a 45 - 45 - 90 isosceles right triangle with two 45 degree angles. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. NASA uses it too! In this article, we have come up with detailed information on different real-life applications of Trigonometry in various fields of our life. If we remember correctly, the problems under this section in our Math books included situations like a shadow of a lamppost falling on the road, tying a rope to a pole, measuring the height of a building, etc. They measure the angle at which the prosthetic limb should be set to provide stability. trigonometry worksheet introduction answers answer key problems. (iv) Naval & Aviation Example Question #1 : Solving Word Problems With Trigonometry A support wire is anchored 10 meters up from the base of a flagpole, and the wire makes a 25 o angle with the ground. "text": "Trigonometry is a very important part of Mathematics that is used in different fields of our life, hence we need triginometry." Lets become the expert triangle expert by solving few problem questions of trigonometry. Trigonometry formulas have applications in various fields such as construction, design, and other branches of engineering. If I increase the larger number by 10, the result will be 5 times the small number. Sine, Tangent, Cotangent, and Cosecant are ODD functions. Compass, pinpoint poles, trigonometric ratios, and various formulas are utilized to determine the exact location of a moving body. Problem 1: Find the length of the side unknown? Once you know the formulas and functions by heart, it is nothing to be afraid of. Draw a picture representing the problem. This is what we will talk about today- how do we use trigonometry in real life? For example, sin /cos = [Opposite/Hypotenuse] [Adjacent/Hypotenuse] = Opposite/Adjacent = tan Therefore, tan = sin /cos is a trigonometric identity. =\frac{\surd 3 -1}{2\surd 2}, Problem 3: Prove that \tan 15 +cot 15 =4, Solution We have, -Criminology and archaeologists used trigonometry Trigonometry is used to set directions such as the north-south or east-west. Bearings are measured clockwise from the northline. Real Life Basic Examples.pdf from MATH TRIGONOMET at University of St Andrews. Marine biologists study marine life such as plants, animals, and other species that reside in the ocean. This website uses cookies to improve your experience while you navigate through the website. Step 4: Mark the angles or sides you have to calculate. 6.01 Trigonometric Identities 6.02 Solving Trigonometric Equations 6.03 Sum and Difference Formulas of Trigonometric Functions 6.04 Double Angle and Half Angle Formulas of Trigonometric Functions 6.05 Law of Sines and Cosines 6.06 Trigonometric Word Problems 6.07 Vectors 6.08 Bonus Video: Law of SinesThe Ambiguous Case HTML, Yes, they use trigonometry to calculate how far a planet or a star is from Earth. Write an equation using the trigonometric function that fits the information. tan = opposite side length = o adjacent length a hypotenuse opposite adjacent. Q5: What are the applications of trigonometry Class 10?Ans: Trigonometry for Class 10 helps us solve problems related to heights and distances, angle of elevation and depression etc. R studio, Not showing working<br />2. Sign up for FREE trial class in a 1:1 environment with a dedicated instructor to check it out. Real life applications of trigonometry | Embibe Exams We also use third-party cookies that help us analyze and understand how you use this website. One common mnemonic is to remember the Indian Chief SOH-CAH-TOA. Everyone knows that Everest has a height of 8848 meters. When you go to the tailor and give your measurements for a dress, they tell you to extend your arm. The sine and cosine functions are fundamental to the theory of periodic functions, those that describe sound and light waves. =\frac{(\surd 3-1)^2+(\surd 3+1)^2}{(\surd 3+1)(\surd 3-1)}\\ Trigonometry is also essential in musical theory and production. The tangent of angle is abbreviated to tan . So, we can say that a triangle has six parts. To start practicing trigonometry, all you need is to click here! Trigonometry is used to set directions such as the east, west, north, south. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. You can determine where exactly a moving vehicle is using the formula and ratio of trigonometry. Confidence. Who Invented Math? "name": "What are the applications of trigonometry Class 10? Seamstresses also use it to determine the angle of darts or the length of cloth required to create a specific shape of a skirt or blouse. From this, computers can produce music, and sound engineers can produce sound effects including pitch and volume. For example, suppose there is a blood droplet a few feet away from the blood splatter. Application of Trigonometry The Involvement should be needed to work in job (example: fashion design). There are six functions of an angle commonly used in trigonometry. Q4: Who is the father of trigonometry?Ans: Hipparchus is considered the father of trigonometry. For example, if a plane is travelling at 234 mph, 45 degrees N of E, and there is a wind blowing due south at 20 mph. They measure the distance first. Music can be studied in terms of sound waves. Mar 9, 2017 - Explore Seul Gi Jang's board "Trig in the Real World" on Pinterest. 7 Examples of Combinational Logic Circuits in Real Life. Step 2. Find the exact value of cos 15. Marine biologists may use trigonometry to determine the size of wild animals from a distance. }. It is also used to shape prosthetic arms and legs as proportions are customized to facilitate operation at maximum potential function. 3. =(\frac{1}{\surd 2})(\frac{\surd 3}{2})-(\frac{1}{\surd 2})(\frac{1}{2})\\ It tells you what direction to take with the compass to get in a straight direction. Vertical Speed: +50sin (30), or 25 miles per hour north. C++, 7 Engaging Activities For Teaching Conjunction In A Fun Way, 7 Effective Examples Of Rewards For Good Behavior At Home, Difficulties Adults With Learning Disabilities Might Face In The Workplace, Calculating projectile motion, vector components, field strengths, etc. How long is the wire, w? Trigonometry is utilized in marine biology to anticipate how far and at what angle a creature or plant is from the scientist. However, if you are looking down from the top of the object, you can use the angle of depression instead and use another side to work out the height. Your GPS receiver helps you to find out your location anywhere on earth. Solution: Given sin (A) = 0.3 M.O.T.3.2: Convert angle measures from degrees to radians (and vice versa) and apply the concept to analyze the formula for arc length. USING TRIG IN THE REAL WORLD. Trigonometry Problems To understand the below question you must know the Trigonometry formulas. Solution to Problem 1: First we need to find the hypotenuse using Pythagora's theorem. 28 Trigonometry Worksheet With Answers - Worksheet Resource Plans starless-suite.blogspot.com. Sailors at sea use sextant tools and compasses to measure the angle of the sun with the horizon at a particular time. So, what are trig functions used for in real . For example, a represents the side opposite angle A, b represents . To be more specific trigonometry is used to design the Marine ramp, which is a sloping surface to connect lower and higher-level areas, it can be a slope or even a staircase depending on its application. When you see him so smoothly glide over the roadblocks. Problem 18. Humans have been drawn to the mysteries of the solar system since the beginning of civilization. The designers and builders of the Egyptian pyramids were greatly influenced by trigonometry. This is an area of math that studies the triangle including the angles and length relationships that define it. Similarly, if you have the value of one side and the angle of depression from the top of the building you can find and another side in the triangle, all you need to know is one side and angle of the triangle. 3. Using trigonometry, we can build relationships in mathematics that contain lengths, heights and angles of different triangles. It is also used to find the distance of the shore from a point in the sea. How do you think sound engineers develop these sound effects with the perfect pitch, volume, and other things? Now try to calculate how tall the tree trunk is. In the given problem,we have to find the angle inclined C. AC = Hypotenuse side . A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60. Sound waves move in a repeating wave pattern that can be visually represented by sine and cosine functions. It helps in determining the angles and distances between structures, and focuses on right-angled triangles, i.e. Real-Life Applications of Trigonometry. It is used in the naval and aviation industries. Share with Classes. In this module, you will apply your knowledge of sine, cosine and tangent to real-world right triangle problems. Putting the values, the exact distance in the Miles unit comes out. Physics use trigonometry For example, to calculate the distance between the Earth and the moon, the circumference of the moon and one of the diameters are used to calculate the arc-length formula. JavaScript Php Ruby Python Mysql, Algebra Equations | Its Types with Solved Examples, Calculus Derivatives -Types & Quotient Rule, Differential Calculus Equations | Formula Sheet, Basics of Algebra Rules with few Examples, Algebra Formula | Algebra Identities and examples, Algebraic Expressions Definition, Examples, and Formulas, Visual Basic Homework Help | VB.net Coding Help, Computer Science Homework Help | Computer Science Help, Java Homework Help | Best Java Assignment Help. What are the numbers? Triangles evenly distribute weight from any direction, when applied correctly. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Next, you measure the objects distance from the observation point and the angle between an imaginary line from the top of the object and the observation point. and few solved trigonometry problems. ", The analyst uses these two measurements to form a triangular structure and, using trigonometric formula and tan function, determine the height at which blood has originated. This formation will represent a right-angle triangle with three sides, perpendicular, base, and hypotenuse. Trigonometry is a branch of mathematics which shows relationship between the length of sides of triangle and its angles. To name a few, trigonometry formula help in construction, marine navigation and archaeology. Now let's see how we get the formula for all the Derivatives of Trigonometric Function. But acquiring a perfect score is not a child's play; students Can you imagine succeeding in your life without a good college? It is only a trick of trigonometry where a point of observation is located first. coding and Resources. Also, you find out that there are different types of phytoplanktons or algae at different depths of the ocean. Discover the Purpose of Mathematics, Benefits of Math: 3 Surprising Ways it Helps Kids, 19 Simple Math Magic Tricks to Intrigue Your Child. "@type": "Answer", Surveyors, architects, astronauts today can hardly do their work without the use of it. Yes, we can and we do also. On the other hand, spherical trigonometry is used to calculate the angles of triangles drawn on a sphere. In this way, Ptolemys Almagest was a watershed moment, serving practical mathematics as Euclids Elements did for theoretical mathematics. Now, set up your trig ratio and solve for a side length: Problem 3. \cot 15=\frac{1}{\tan 15}=\frac{\surd 3+1}{\surd 3-1}\\ They are in "feet", so feel free to substitute "metres" for "feet" when you watch the videos.
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