An identification of the copyright claimed to have been infringed; Because we want to find the change in height (also called elevation), we want to determine the difference between her ending and starting heights, which is labelled x in the diagram. {/eq}. If you've found an issue with this question, please let us know. This trigonometry word problems answers, as one of the most functional sellers here will certainly be accompanied by the best options to review. Already registered? in Mathematics from Florida State University, and a B.S. We see the shadow on the ground, which corresponds to the base of our triangle, so that is what we'll be solving for. Problem 18. Next, think about which trig functions relate our known angle, 22o, to the base (or adjacent) and the opposite sides of the triangle. United States Instructions Step-by-step Instructions. Law of Sines Example Problem Science Notes and Projects, Law of Sines or Sine Rule (solutions examples videos), law of sines Miss Sahady PSHS Class Website, Law of Sines Worksheet (pdf) with answer key and model Label the angle of elevation as 25o, the height between the ground and where the wire hits the flagpole as 10 meters, and our unknown, the length of the wire, as w. Now, we just need to solve for w using the information given in the diagram. your copyright is not authorized by law, or by the copyright owner or such owners agent; (b) that all of the Thus, if you are not sure content located \dfrac{\sin(30^\circ)}{45} {}&= \dfrac{\sin(20^\circ)}{x}\\ Practical Application: Social Media Networking Checklist, Picasso's Guernica: Definition, Symbolism & Analysis, The Myth of Sisyphus by Albert Camus: Allusion & Quotes. How far did they drive from Gary's to get ice cream and how far did they drive from the ice cream shop back to Tamara's? The law of sines is expressed as follows: a sin ( A) = b sin ( B) = c sin ( C) where, a, b, c represent the lengths of the sides of the triangle and A, B, C represent the angles of the triangle. Massachusetts Institute of Technology, Bachelor of Science, Physics. misrepresent that a product or activity is infringing your copyrights. How far from the boat is the top of the lighthouse? You might not require more grow old to spend to go to the ebook commencement as capably as search for . Next, we need to think of the trig function that relates the given angle, the given side, and the side we want to solve for. \end{align} Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, How to Solve a Word Problem Using the Law of Sines, {eq}\dfrac{\sin(28^\circ)}{6.8} = \dfrac{\sin(20^\circ)}{x} If she drives 4000 meters along a road that is inclined 22o to the horizontal, how high above her starting point is she when she arrives at the lookout? Examples: An airplane over the Pacific sights an atoll at a 20 angle of depression. Therefore: (Use a calculator in degree mode to find thatafter rounding to two decimal places). Solved word problems, tests, exercises, and preparation for exams. {/eq} are the angles of a triangle and {eq}a, \ b, \ c The law of sines says {eq}\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b} = \dfrac{\sin(C)}{c} as acuteness of this word problems with solutions in trigonometry can be taken as with ease as picked to act. To solve word problems involving trigonometry you should always follow the same process. In feet, how far up the side of the house does the ladder reach? Your name, address, telephone number and email address; and Law of Sine and Cosine Word Problems Worksheet, Word Problems Law of Sines and Cosines Google, 8. Trigonometry Word Problems. If you're seeing this message, it means we're having trouble loading external resources on our website. Problem 1 : A farmer wants to purchase a triangular shaped land with sides 120 feet and 60 feet and the angle included between these two sides is 60 . Write down known. A description of the nature and exact location of the content that you claim to infringe your copyright, in \ Just snap a picture of the question of the homework and CameraMath will show you the step-by-step solution with detailed explanations. From the ice cream shop, they can take another road that leads back to Tamara's house that forms a 28 degree angle with the road they were on. To solve this problem, we need to create a diagram, but in order to create that diagram, we need to understand the vocabulary that is being used in this question. 10 is opposite this angle, and w is the hypotenuse. Find the length of a side or measure of an angle using Law of Sines. Is it the hypotenuse, or the base of the triangle? With the help of the community we can continue to copyright 2003-2022 Study.com. If no diagram is given, draw one yourself. Law of Sines Substitute. Step 2: Set up an equation using the law of . Determine the smallest integer p for which the equation 4 sin x = p has no solution. Think about when you look at a shadow. a. The sine function relates opposite and hypotenuse, so we'll use that here. Maya Architecture Overview & Examples | Pyramids, Temples Immunologic & Serologic Characteristics of Fungal & Molecular Testing & Diagnostics for Lymphoma. What advice would you give yourself for the next time you solve word problems with law of sines and cosines? She also holds a current teaching certificate in the state of Idaho. Practice: General triangle word problems. Law of sine word problems with solutions pdf The Chapter 8 Resource Masters includes the core materials needed for Chapter 8. Law of Sines/Cosines Word Problems 1. which specific portion of the question an image, a link, the text, etc your complaint refers to; Click to see solution. Plus, get practice tests, quizzes, and personalized coaching to help you As a member, you'll also get unlimited access to over 84,000 An error occurred trying to load this video. Looking at what we have now, we see that we only need the first two parts of our law of sines to find our answer: a /sin A = b /sin B. United States Instructions Step-by-step Instructions, Manual del tablero de instrumentos del jeep grand cherokee. Click to see solution. Solution : To find the missing side, let us use cosine formula. We can fill in all three angles, since we know two of the angles and that the angles of a triangle must add up to 180 degrees. A ladder is leaning against a vertical wall makes an angle of 20 with the ground. The foot of the ladder is 3 m from the wall. While the blue line is drawn on the left hand side in the diagram, we can assume is it is the same as the right hand side. Trigonometry Word Problems . In right triangle ABC, where angle A measures 90 degrees, side AB measures 15and side AC measures 36, what is the length of side BC? {/eq} are the sides opposite those angles, respectively. Copyright 2005, 2022 - OnlineMathLearning.com. Ambiguous case two solutions Law of Sines Word Problems #2 5 5 Law of Sines Word Problems Law of Sines - Application/Word Problem, Ex 1 Law of Sines Word Problem 2 Day 12 CW (5) Using the Law of Sines to Solve Word Problems 3.1 Sine Law (Word Problems) Law of Cosines: Word Problems The road she is driving on is the hypotenuse of our triangle, and the angle of the road relative to flat ground is 22o. Decide whether you will need Pythagoras theorem, sine, cosine or tangent. Infringement Notice, it will make a good faith attempt to contact the party that made such content available by This is the currently selected item. The number of possible sines is infinite. Send your complaint to our designated agent at: Charles Cohn Tamara leaves her apartment and drives west for 6.8 miles to meet her friend Gary. Model Problems. After that he increased his speed by 2 km/hr. All other trademarks and copyrights are the property of their respective owners. Then use a calculator to evaluate and round to two decimal places. Law of Sines: The law of sines states that for any triangle {eq}\Delta ABC Word Problems. Log in here for access. Consider whether you need to create right triangles by drawing extra lines. as A kite is flying at a height of 65 m attached to a string. Solve word problems that involve general (non-right) triangles using the law of sines and law of cosines. y & = \dfrac{45\sin(130^\circ)}{\sin(30^\circ)}\\ From the top of a lighthouse that sits 105 meters above the sea, the angle of depression of a boat is 19o. A D B C x 65o 30o 80o 12 10 Mar 39:18 AM Maggy wants to find the height of the tree outside her house. Round your answer to the nearest thousandth. You are standingfeet from the base of the platform, and the angle of elevation from your position to the top of the platform isdegrees. The cable makes an angle of 60 degrees to the ground. Therefore, the taller building is104.6 feet tall. The shorter building is 40 feet tall. Matilda's Telekinesis: How Did Matilda Get Her Powers? As this sine law word problems with solutions, it ends in the works bodily one of the favored book sine law word problems with solutions collections that we have. The international standard pitch has been set at a frequency of 440 cycles/second. \dfrac{\sin(28^\circ)}{6.8} {}&= \dfrac{\sin(132^\circ)}{y}\\ \dfrac{\sin(28^\circ)}{6.8} {}&= \dfrac{\sin(20^\circ)}{x}\\ We have: (Use a calculator and round to two places to find that). We have two unknown values, and so will need two equations. We know thatand. means of the most recent email address, if any, provided by such party to Varsity Tutors. 1) Find AC 24 A C B 118 22 2) Find AB 7 C A B 53 44 3) Find BC 27 C B A 51 39 4) Find AB 9 B C A 101 63 5) Find BC 16 A B C 93 58 6) Find mC 21 26 16.1 A C B 88 7) Find mC 24 20 C 29 A B 82 8) Find mC Worksheets are Extra practice, Find each measurement round your answers to the, Law of sines work, Find each measurement round your answers to the, Law of sines, Law of sineslaw of cosines word problems, Law of sines practice work, Chapter 14 packet trigonometric applications. Isolate . To find that, we need to addfeet. That means that we want to determine the length of the hypotenuse, or red line labelled SlantRange. To make sense of the problem, start by drawing a diagram. In feet, how tall is the flagpole? the 6. How to use the Law of Cosines, Proof for the Law of Cosines, how to use the Law of Cosines when given two sides and an included angle, when given three sides, how to solve applications or word problems using the Law of Cosine, examples and step by step solutions Law of Sine/Cosines Word Problems Instructure, Title: Law of Sines and Law of Cosines Word Problems Author: Bob Mulligan Created Date: 9/24/2015 4:23:06 PM ChillingEffects.org. link to the specific question (not just the name of the question) that contains the content and a description of Trigonometry Word Problems (solutions, examples, videos) Solve word problems by modeling real-world (and not-so-real) situations as right triangles and using trigonometry. In the following example you will find the measure of an angle of a triangle using Law of Sines. y & \approx 68.94 Step 1: Find the values of the givens. Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. Label all known sides and angles. Cancel any time. x & = \dfrac{45\sin(20^\circ)}{\sin(30^\circ)}\\ Solution: We can find the height of the monument by using the tangent ratio and then adding the eye height of . Problem 6. Sine and Cosine Law Word Problems (Solutions).notebook 4 January 15, 2016 Jan 128:45 AM 5)Bailey and Riley are standing 5250 feet apart on a straight, horizontal road. 360cm26. A ladder that isfeet long is resting against the side of a house at an angle ofdegrees. Three friends are measuring out a triangular plot of land with rope in a backyard to make a garden. Homeschool Your Child for Free LauraMaery Gold 2009-08-04 Provide a solid education at home We will use these steps, definitions, and equations to solve word problems using the law of sines in the following two examples. The angle of elevation from Bailey is 600 and from Riley is 750. Word Problems Stephen K. Reed 1998-12 Research by cognitive psychologists and mathematics educators has often been compartmentalized by departmental boundaries. Find the height of the pole to the nearest foot. As with other trig problems, begin with a sketch of a diagram of the given and sought after information. Economic Scarcity and the Function of Choice, Crow Native American Tribe: History, Facts & Culture, The Lakota of the Plains: Facts, Culture & Daily Life, Slavic Mythology: Gods, Stories & Symbols, Otomi People of Mexico: Culture, Language & Art, Airway Resistance: Definition, Formula & Issues, Organic Organizational Structure: Definition & Examples, General Social Science and Humanities Lessons. If you got one of the incorrect answers, you may have used sine or cosine instead of tangent, or you may have used the tangent function but inverted the fraction (adjacent over opposite instead of opposite over adjacent.). Using . Sine and Cosine Law Word Problems (Solutions).notebook 3 January 15, 2016 Oct 208:48 AM Example 3: Find x to the nearest unit. Brianna has tutored high school and college level math for over five years. x & \approx 30.78 When the angle of elevation of the sun isdegrees, a flagpole casts a shadow that isfeet long. Tabor College, Bachelor in Arts, Mathematics Teacher Education. Then, set up: (using a calculator in degree mode and rounding to two decimals we get that). However, we can instead find the distance, and then add that to the 40 foot height of the shorter building to find the entire height of the taller building. The shorter building is 55 feet tall. 58.6m If you're seeing this message, it means we're having . MidAmerica Nazarene University, Masters in Education, Educati University of Central Florida, Bachelor of Science, Biotechnology. We get: (where d is the distance between the top of the lighthouse and the boat), (using a calculator in degree mode and rounding to two digits, we get that). The sides are denoted using lower case letters with respect to their opposite angle. \end{align} -Level Problem: 6. Answers: 1. Track your scores, create tests, and take your learning to the next level! From the ground, she measures the angle of elevation to the top of Just think about it. You may need to use a calculator to finish solving and round to the specified number of decimal places if values in the problem are not on the unit circle. Word Problems - Symptoms & What Is a Primary Care Physician? All of the materials found in this booklet are included for viewing and printing on the TeacherWorks Plus TM [] They see a hotair balloon between them directly above the road. We know that sine of a given angle is equal to the opposite divided by the hypotenuse, and cosecant of an angle is equal to the hypotenuse divided by the opposite (just the reciprocal of the sine function). If you thought tangent (or cotangent), you are correct! problem solver below to practice various math topics. If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one For E D F, find the length of side f, given that E = 33 , F = 121 , d = 4 and e = 5. II. Show Step-by-step Solutions. Word Problem Using Sine Law 1/9 [PDF] Word Problem Using Sine Law Law of Sines or Sine Rule (video lessons, examples and The Law of Sines is also known as the sine Chapter 2 Epilogue Trig Word Problems - Math with Mr. K. Sine and Cosine Law Word Problems (Solutions).notebook 4 January 15, 2016 Jan 128:45 AM 5)Bailey and Riley How high is the taller building? When you see a shadow, you are seeing it on something else, like the ground, the sidewalk, or another object. Angelina and her car start at the bottom left of the diagram. 500 per sq.ft, find the amount he needed to purchase the land. 2007-2022 All Rights Reserved, San Francisco-Bay Area Trigonometry Tutoring, San Francisco-Bay Area Trigonometry Tutors. Try refreshing the page, or contact customer support. Check that your answer is reasonable. It's not all about sines. Sine - word problems. Step 3: Solve for the missing side. 8. Angelina just got a new car, and she wants to ride it to the top of a mountain and visit a lookout point. Find the distance between the two towns and the initial speed of the biker. If the height of the cliff is 80.0 m, find the distance between A and B. If the two friends holding the 20 and 130 degree angles are 45 feet apart, how long are the other sides of the triangle? Round to the nearest whole degree. To find that, we need to addfeet. Step 3: Solve the equation from step 2 using cross-multiplication. law of sines Miss Sahady PSHS Class Website, United States tutorials Step-by-step Guidelines 2022, United States tutorials Step-by-step Guidelines, Manual de bioseguridad en centros de salud. on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. 2. To solve this problem, let's start by drawing a diagram of the two buildings, the distance in between them, and the angle between the tops of the two buildings. Make sure to round toplaces after the decimal. trig word problem law of cosines help yahoo answers, law of sines and cosines word problems, the law of sines math is fun maths resources, solve triangles using the law of cosines practice khan, general triangle word . Trigonometry Word Problems (Solutions) 1) One diagonal of a rhombus makes an angle of 29 with a side ofthe rhombus. A person observes that from point A, the angle of elevation to the top of a cliff at D is 30. From the roof of the shorter building, the angle of elevation to the edge of the taller building is 48o. One Angle and the Law of Cosines Huntsville TX Try the free Mathway calculator and trigonometry-word-problems-and-solutions 3/3 Downloaded from ads.independent.com on November 5, 2022 by guest Problem Solving (12 hours): This course will cover Root Cause Analysis (RCA) which is a popular and often-used technique that helps people answer the question of why the problem occurred in Law of Sines and Cosines Worksheet PDF DSoftSchools. A post is supported by two wires (one on each side going in opposite directions) creating an angle of 80 between the wires. We welcome your feedback, comments and questions about this site or page. Step 1: Draw a picture representing the situation in the word problem. I'm not saying that everything in this book is good. To solve this problem, first set up a diagram that shows all of the info given in the problem. If Varsity Tutors takes action in response to Show Answer. {/eq}. {/eq} miles and the {eq}28^\circ a If the plane is 435 m above water, how many . y & = \dfrac{6.8\sin(132^\circ)}{\sin(28^\circ)} Trigonometry Word Problems (Solutions) 1) One diagonal of a rhombus makes an angle of 29 with a side ofthe rhombus. {/eq}. \dfrac{\sin(30^\circ)}{45} {}&= \dfrac{\sin(130^\circ)}{y}\\ St. Louis, MO 63105. {/eq} with sides {eq}a, \ b, \ c So the Law of Sines is used to Example problems. Two buildings with flat roofs are 80 feet apart. Mathematically, it is stated as n 1 sin 1 = n 2 sin 2. where n i . Problem 5. The friends are about 30.78 feet and 68.94 feet apart. Using Danielson's Framework for Teaching in the Classroom. Remember that this is not the full height of the larger building. {eq}\begin{align} trigonometry-word-problems-solutions 1/1 Downloaded from edocs.utsa.edu on November 2, 2022 by guest Trigonometry Word Problems Solutions Thank you unconditionally much for downloading trigonometry word problems solutions.Maybe you have knowledge that, people have see numerous times for their favorite books considering . 7. {/eq}, {eq}\dfrac{\sin(28^\circ)}{6.8} = \dfrac{\sin(132^\circ)}{y} Start by finding: Remember that this is not the full height of the larger building. Example 2: Find . {eq}\begin{align} {/eq} where {eq}A, \ B, \ C We'll call this base b. answers-trigonometry-problems 1/2 Downloaded from classifieds.independent.com on November 8, 2022 by guest Answers Trigonometry Problems . {/eq}, as shown in the image below, it is true that {eq}\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b} = \dfrac{\sin(C)}{c} Embedded content, if any, are copyrights of their respective owners. succeed. Title: Law Of Sines Word Problems With Solutions Keywords: Law Of Sines Word Problems With Solutions Created Date: 11/3/2014 3:49:16 PM Sample Problems for Snell's Law Important Information Snell's Law describes how light bends when traveling from one medium to the next. The Ambiguous Case ednet.ns.ca DSST Introduction to World Religions: Study Guide & Test GACE Marketing Education (546): Practice & Study Guide, Criminal Justice for Teachers: Professional Development, Orange Juice in Life of Pi: Quotes & Symbolism, 'War is Peace' Slogan in 1984: Meaning & Analysis. From the roof of the shorter building, the angle of elevation to the edge of the taller building is 32o. information described below to the designated agent listed below. in Mathematics from the University of Wisconsin-Madison. This is why you remain in the best website to look the incredible book to have. Also find the perimeter of the land. person at point B, notes that the angle of elevation to the top of the cliff is 45. Sort by: Top . After reviewing the answers and solutions, what were your misconceptions? 360 c. 36 Application to Trigonometric Functions . either the copyright owner or a person authorized to act on their behalf. For the first equation, we can cross multiply and solve for {eq}x They drove about 4.95 miles from Gary's to the ice cream shop and about 10.76 miles from the ice cream shop back to Tamara's. 30-60-90 The longer leg of a 30-60-90 triangle measures 5. She has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S. Two buildings with flat roofs are 50feet apart. DSoftSchools Free Worksheets for Teachers and Students 11 Interesting word problems with solutions involving the law of sines and cosines. She has a bachelors degree in mathematics education from Brigham Young University-Idaho. SINUSOIDAL GRAPHS AND WORD PROBLEMS The tuning fork is a device used to verify the standard pitch of musical instruments. lessons in math, English, science, history, and more. Kathryn has taught high school or university mathematics for over 10 years. It only takes a few minutes to setup and you can cancel any time. For example, divide an isosceles triangle into two congruent right triangles. The four general steps of the process are listed below, but they are in the wrong order! . or more of your copyrights, please notify us by providing a written notice (Infringement Notice) containing For example, know a side-sine pair given ASA. 32.23. Explanation: To make sense of the problem, start by drawing a diagram. If the inclination of the string with the ground is 31, find the length of string. {/eq}. Correct answer: 23.81 meters. Again, only the calculation for part a is shown below; the rest are similar. Math questions with answers. {/eq} angle, since we have all the information for that angle and the side opposite it. You can draw the following right triangle using the information given by the question: Since you want to find the height of the platform, you will need to use tangent. The formula for the law of cosines is an equation that relates the lengths of two sides of a triangle to the angle between the two sides. It only takes a few minutes. Step 2: Set up an equation using the law of sines to solve for the unknown value. {/eq}, {eq}\dfrac{\sin(30^\circ)}{45} = \dfrac{\sin(130^\circ)}{y} II. \sin(28^\circ)y & = 6.8\sin(132^\circ)\\ Native Americans & European Exploration of Americas, Holt McDougal Modern Biology Chapter 44: Animal Behavior, Eukaryotes for the MCAT: Tutoring Solution, Virus Structure & Life Cycle for the MCAT: Tutoring Solution. 604.4ft5. Very frequently, angles of depression and elevation are used in these types of problems. Find the inverse. Write a rule in the form f(t) = A sin Bt that expresses this oscillation where t represents the number of seconds. Find the height of the balloon. These materials include worksheets, extensions, and assessment options. Label all known sides and angles. The altitude or blue line is opposite the known angle, and we want to find the distance between the boat (point B) and the top of the lighthouse. Problem 17. Merging together the given info and this diagram, we know that the angle of depression is19oand and the altitude (blue line) is 105 meters. In order to find the height of the flagpole, you will need to use tangent. - Definition & Shortage, Collodi's The Adventures of Pinocchio: Characters & Themes. Next, consider which trig function relates together an angle and the sides opposite and hypotenuse relative to it; the correct one is sine. Sinceis aright angle, we can use the Pythagorean Theorem, whereis the hypoteneuse: A support wire is anchored 10 meters up from the base of a flagpole, and the wire makes a 25o angle with the ground. When the sun is 22o above the horizon, how long is the shadow cast by a building that is 60 meters high? Solution: Here, simply use the same process as the previous practice problem, but use the reciprocal ratio of radians and degrees. 19.12. Both equations will use the {eq}6.8 Please be advised that you will be liable for damages (including costs and attorneys fees) if you materially Round your answers to the nearest tenth. Draw a sketch: 7.2" Label the rest: 7.2" Solve: 7.2" Since it is a rhombus, we know all the sides are 7.2". While waiting for your sister to finish her bungee jump, you decide to figure out how tall the platform she is jumping off is. Mark the angles or sides you have to calculate. The answers for these pages appear at the back of this booklet. Sine Function Word Problems A word problem involving the trigonometric ratio of sine to calculate the height of a pole Example: A 55ft wire connects a point on the ground to the top of a pole. 5.3m 4. For example, a represents the side opposite angle A, b represents . \end{align} SOLVING OBLIQUE TRIANGLES THE LAW OF COSINES, One Angle and the Law of Cosines Huntsville TX, General triangle word problems (practice) Khan Academy They are standing at each vertex of the triangle. We need to ask ourselves which parts of a triangle 10 and w are relative to our known angle of 25o. All rights reserved. The formula for the law of cosines is: a 2 = b 2 + c 2 2 b c cos ( ) b 2 = a 2 + c 2 2 a c cos ( ) c 2 = a 2 + b 2 2 a b cos ( ) where, a, b, c represent the lengths of the sides of the . Braingenie Word Problems – Find the distance, TRIGONOMETRY 3 Trigonometry Self-Paced Review Module As you probably know, trigonometry is just the measurement of trian-gles, and that is how it got started, in connection with surveying the Round your answer to two decimal places. an How high is the taller building? A biker covered half the distance between two towns in 2 hr 30 min. One friend is holding two ends of rope at a 30 degree angle, another is holding at a 20 degree angle, and the last is holding at 130 degrees. Varsity Tutors. \end{align} Therefore the shadow cast by the building is 150 meters long. Therefore the change in height between Angelina's starting and ending points is 1480 meters. Mathematics: Word math problems . Trig Law Of Sines Cosines Word Problems chapter 14 packet trigonometric applications, word problems with sine and cosine . I. Some of the worksheets below are Law of Sines and Cosines Worksheet in PDF, 4 Cases where Law of Cosines is the best choice, Interesting word problems, Skip to content. {/eq}. A practical application of the trigonometric functions is to find the measure of lengths that you cannot measure. The hypotenuse is the longest side in a right triangle. You can draw the following right triangle from the information given by the question. Round your answer to the nearest hundredth. Now, we can finally look at what circles have to do with trigonometry. What is the length of . Solving Word Problems Using the Law of Sines. Law of Cosines Worksheet. For the second equation, we can cross multiply and solve for {eq}y A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require Show Answer. The Show the sizes of the other angles and the lengths of any lines that are known.
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