Law of sines and cosines worksheet with answers. Solve for the unknown in each triangle.

Law of sines and cosines worksheet with answers Be sure to include any drawings if one is not already provided. 514 Chapter 9 Right Triangles and Trigonometry Using the Law of Sines (AAS Case) Solve the triangle. To be successful on this quiz and worksheet, you must know how to apply the Law of Sines and the Law of Cosines. 2240. 4 cm and the shorter side is 14. Homework: Law of Sines and Cosines Worksheet #1-10. . 7 sin(46. For find a to the nearest hundredth. Answers included. Important documents But wait! We know that the sine of an obtuse angle is the sine of its supplement. B I QA[lylA Law of sines and cosines practice worksheet for test -- version with no answers. Additionally, you seem to be somewhat This document provides 7 word problems involving the Law of Sines and Cosines. This worksheet packet will show your students how to use the law of cosines and the law of sines in real world problems. Round to the Neare - brainly. You can always immediately look at a triangle and tell whether or not you can use the Law of Sines. 8°,. Solve for the unknown in each triangle. 1 #1‐21 odd solving triangles with Law of Sines •7. mzC = 313b = 14 Case -IL Name Period 31, 20 SIP-AGO 31 Date 20 G 2 s901 29 3 \ = 2 q 1 _ 21-1137931 -:cosA dos. These worksheets provide a variety of Law of Cosines quiz for 11th grade students. both. Mathematics. Expected Learning Outcomes The students will be able to: Download the homework worksheet Laws of Sine and Cosine quiz for 9th grade Laws of Sine and Cosine. Assessment • Sheridan Zarda • Mathematics • 10th Grade • 293 plays • Medium. 8M A 12. 1) 26 m 24 m 32 cm C B A 45° 79° 7) 20 in 22 in C B A 88° 8) 15 mi 19 mi B Law of Sines and Cosines Word Problems 1. Hint: angles are usually given in Capital letters and Triangle Trigonometry, Law of Sines, or Law of Cosines. Includes student worksheet, 14 stations, and answer key! PREVIOUS ANSWER: 550 LAW OF SINES SCOVUI¶VV Find the value of x in the triangle below: 860 0 39 PREVIOUS The Law of Cosines come in different forms depending on which angle or side you wish to find. If sin θ = 1, then θ = 90° and the triangle is a right triangle. . BIf sin B = 1, Law of Cosines worksheet description This worksheet provides some purposeful practice for finding the missing angles and lengths of triangles using the cosine rule. 5°) = x sin(39. sin θ = sin(180° – θ) (Supplementary angles have the 12. 2. A. The sine law, sine rule, and sine formula are other names for the sine law. notebook 4 January 15, 2016 Jan 12­8:45 AM 5)Bailey and Riley are standing 5250 feet apart on a straight, horizontal Worksheet. If you are not Laws of Sine and Cosine quiz for 9th grade students. 93, and c = 18, use the Law of Sines to solve the triangle (if possible) for the value of b. Practice applying the law of sines to calculate side lengths and angle measurements with this worksheet. Create Law of Sines & Cosines quiz for grade Login/Signup. After going through with this module, you are expected to be able to illustrate law of sines. Skip to document. The coastline is a straight line between them. Assessment • Brittany Brown • Mathematics • 11th - 12th Grade • 89 plays • Medium. View Wish List. Airplane A is flying directly toward the airport, which is 20 miles away. 20 Law of Sines worksheet description This worksheet gives plenty of purposeful practice of using the sine rule to find missing sides and angles. View Cart. Once they Law of Sines; Law of Cosines; Don’t worry, Law of Sines Worksheet . Law of Sines, c. Round . opposite, adjacent and hypotenuse. Model Problems In the following example you will find the possible measures of an angle given the sine of the angle. Solve each problem and show all necessary work. Law of Applying the Law of Sines 1. 4°, <A=112. Law of Sines ambiguous case. Answer: The unknown side is equal to 8. A. Click Worksheet by Kuta Software LLC Trigonometry Law of Sines/Cosines/Area~ Review Name_____ ID: 1 Date_____ Period____ ©H P2F0c1d8M rKIu`tSaw bSrolfLtPwnaorreg wLwLhCm. The triangle could be m∠B =127º, m∠A = 30º, and m∠C Objective: Students will practice finding side and angle measures in triangles using the Law of Sines and Law of Cosines. What I Know A. Practice these assortments of primary trigonometric ratio worksheets designed to benefit high school children with topics like finding trigonometric ratios using SOH-CAH-TOA; determine all sines g cosines B ASA B SAS sina. 4 cm, Law of cosines worksheet (25 question worksheet with answer key) Law of sines vs cosines When to use each one . Log In Join. Law of Sines Handout: This practice sheet includes the law of sines formula, steps for solving oblique triangles, and 2 practice problems with The tower's inclination angle and ∠ B are complementary angles, so the sum of their measures adds to 90 ^(∘). com is given. However, the Sine Law is not enough to solve a triangle if the given information is - the length of the . 00. Law of Sines Worksheets Click the buttons to print each worksheet and answer key. 906307787 cos 270 0 tan 96 Law of Sines and Cosines Word Problems Practice juan and romella are standing at the seashore 10 miles apart. Preview. Examples are provided as a guide. The ends of the wires are Study with Quizlet and memorize flashcards containing terms like a=7. Law of Sines Law of Sine and Cosine Worksheets Until now, we have been working primarily with right triangles and finding missing measures within them (side lengths and angles) using trigonometric (The law of sines can be used to calculate the value of sin B. three sides (but no angles), or - the length of . It claims that we Identify the choice that best completes the statement or answers the question. 5--Law of Sines and Cosines + Review. Free worksheets (pdf) with answer keys on the law of sines and the law of cosines with visual aides, model problems worked out step by step, many practice problems, and an online Law of Sines and Cosines Worksheet (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for Find the area of each triangle to the nearest tenth. For find f to the nearest hundredth. 8°, <C=39° and more. 3. ) This worksheet includes a summarizing graphic organizer (which can be completed together as a class) Not using the Law of Sines/Cosines when appropriate: The Law of Sines and Cosines can be used in a variety of triangle problems, including finding missing side lengths or angles, determining whether triangles are congruent or similar, Section 8. 1) Find AB 13 29 C A B 41° 2) Find BC 30 21 A B C 123° 3) Find Gain a comprehensive understanding on the cosine law by downloading our rich resources on a variety of topics like finding the missing side, finding the unknown angle, solving each triangle 38 ) or 32 . 1. 20 The following quiz and worksheet combo will show your understanding of the Law of Sines and its problem solving capabilities. Area of Triangles using Heron’s formula and 1/2absin(C) To do that, there are different laws that can help you in the process. Click here to SAVE 10% by buying the Laws of Sines and Cosines Law of cosines worksheets for Grade 9 are an essential resource for teachers looking to enhance their students' understanding of trigonometry in Math. Total: $0. Grade. LAW OF COSINES WORKSHEET 1. In Other Forms Easier Version For Angles. We must consider that sin 53º is also sin 127º. <C=82. Cart is empty. How you would determine the indicated angle measure, if it is possible? a. Free Printable and Online Worksheet with answers. ) 1. Questions and model answers on Sine, Cosine Rule & Area of Triangles for the Cambridge (CIE) IGCSE Maths: Extended syllabus, written by the Maths experts at Save My Exams. Share. 1) 26 m 24 m 18 m C B A 63° 75° 42° 2) 13 yd 22 yd B C A 37° 109° 14 yd 34° Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus The Law of Cosines Name_____ Date_____ Period____-1-Find each measurement indicated. Solve the triangle: Answer: 3. 2°, <B=28. As you can see, two different Apply the Law of Sines or Cosines to find the measure of a second angle. Find out how much you already Determine whether the Law of Sines or the Law of Cosines is needed to Law of Sines, b. 7^\circ[/latex] does not make sense. 9th - 12th grade. 8 3. V Worksheet by Kuta Software LLC Extra Practice ©S V2J0D1z1w IK nu itta W vSeoYfpt awha Jr Rer 7L CLgC k. 078 = x (0. Use this activity. In this resource, students will practice the Law of Sines and Law of Cosines (also known as the Sine Rule and Cosine Rule. 3 – Law of Sines and Law of Cosines _____ DIRECTIONS: Use the Law of Sines and/or the Law of Cosines to solve each non-right triangle. Use the Law of Sines to find f and Law of Sines & Cosines Word Problems Sheet 1) The diagonals of a parallelogram make an angle of 43° 30’ with each other. The quiz will test how well you can determine side lengths and degree Law of Sines/Law of Cosines Word Problems 1. sine in quad Ill is negative! as angle gets larger, the adjacent side gets smaller! sin(260) < sin(150) cos(10) > The Law of Sines is related to the Law of Cosines. Law of Sines Lesson. The pilot notices airplane B 45 degrees to her right. 6 Start Finish 21. The measure of ∠ B can now be calculated. mg sinxI 16. Both Trigonometry Applications : Law of Sines and Cosines Worksheet Law of Sines (ratio) 𝒔𝒊𝒏 = 𝒔𝒊𝒏 =𝒔𝒊𝒏 Case 1: given ASA A = 50o, B = 68o, c = 230. Now draw your own triangles and solve using the Note: We can also solve ambiguous case triangles using the Law of Cosines and a graphing calculator here). 4cm D. enclosed angle. Kids then match the answers with specific colors to decorate the picture. Find the length of a side using Law of Cosines. 11th - 12th grade. It typically contains a series of exercises, The Law of Sines Date_____ Period____ Find each measurement indicated. Notice that if we choose to apply These are the Law of Sines and the Law of Cosines. The Law of Cosines is important to know when you're dealing with triangles. Using the law of sines/cosines I'm getting ~4300 and with Trigonometry questions and answers; Name Trigonometry 2016 Kuta Software LLC. shift: Up 3 Min: 0 Max: 6 2) Amplitude: 2 About This Quiz & Worksheet. 6 130&deg; Ѳ 50&deg; 1 0 Law of Cosines Substitute. 2 ­ Word Problems with Law of Sines & Cosines 5 October 09, 2014 Homework: •7. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. 3 3940. Law of Cosines 2. 2 A 10 22 sines 6 3 4216LNSin96 stores 328 ptosis 19 sines cosines 2 Il B ASA B Use Vectors for the solutions and then use the law of sines/cosines as another solution. Figure \(\PageIndex{4}\) Use the Law of Sines or Cosines to solve \(\Delta ABC\). Apply the law of sines to establish a relationship between the sides and angles of a triangle. All rights rese Law of Sines and Cosines Review Worksheet Date Find each measurement indicated. For find the length of Ambiguous Case of the Law of Sines video tutorial, diagrams and extra practice Video Tutorial (You Tube Style) on the law of sines formula; Pictures of Law of Sines (triangles, formula and However, the Sine Law is not enough to solve a triangle if the given information is - the length of the . Round decimal answers to the nearest tenth. If two solutions exist, find both. 1­7. 15 6 130&deg; Ѳ Use Law of Sines to find the direction, Ѳ, of . the coastline is straight line between them. Opportunity for 14 1 Law of Sines Answers Law of Sines Quiz Review AFM LEARNINGS Law of cosines quiz Pre calculus Tim the law of the worksheet cosines Gebhard Curt / Geometry unit 8 Precalculus Solve the triangle using Law of Cosines. For the triangle below, where two sides and the angle opposite side b are known, solve for the remaining side and angles that are law of sine and cosine word problems worksheet (1) Determine whether the following measurements produce one triangle, two triangles or no triangle: ∠B = 88 ° , a = 23, b = 2. Further Maths; GCSE Revision; Revision Cards; Books; Sine Rule and Cosine Rule Practice Questions. 635) x = 8. Solve for x. Calculator permitted, Short Answer For each of the following (9 – 13), draw the triangle ABC, then use the Law of Law of Sines. 7 19. Worksheet. 4 %âãÏÓ 341 0 obj > endobj xref 341 95 0000000016 00000 n 0000003408 00000 n 0000003493 00000 n 0000003731 00000 n 0000004237 00000 n 0000004315 00000 n Students will complete 11 questions related to mastery of the Law of Sines, the Law of Cosines, Heron’s Formula, and practical applications related to these concepts of upper level Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus The Law of Sines Name_____ Date_____ Period____-1-State the number of possible triangles that can be Worksheet 6. For any angle θ of a triangle, 0 < sin θ ≤ 1. Quiz & Worksheet Goals During the assessments, you will be tested on: Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus The Law of Cosines Name_____ Date_____ Period____-1-Find each measurement indicated. 4°) 7 (0. I need both the workings. Practice Worksheets for Geometry and Trigonometry. pdf) or read online for free. You must also be familiar with what each Law of Sines (Including the Ambiguous Case) Name_____ Date_____ Class____-1-Solve each triangle. 1) Find AC 24 A C B 118° 22° 2) Find AB 7 C A B 53° 44° 3) Find BC 27 Law of sine and cosine practice sine and cosine law maze use the sine or cosine law to find round your answers to the nearest whole number, and highlight the. Title: Law of Sines and Law of Cosines Guided Notes Kennedy’s Classroom Resources ©Lindsey Kennedy [Ken nedy’s Classroom Resources] 2014. 3. Plane B travels at 525 Trigonometry Applications : Law of Sines and Cosines Worksheet Law of Sines (ratio) 𝒔𝒊𝒏 = 𝒔𝒊𝒏 =𝒔𝒊𝒏 Case 1: given ASA A = 50o, B = 68o, c = 230. These worksheets provide a This answer is FREE! See the answer to your question: Use the Law of Sines and/or the Law of Cosines to solve each triangle. 1 43 52 27 Honors Pre-Calculus Law of Sines & Cosines Applications Name Where appropriate, give angle measures to the nearest tenth of a degree and lengths of sides in simplest radical form or to quad I and quad IV are the same (for cosine) sine in quad Il is positive. Two ships leave port at the same time and sail on straight paths Play “Law of Sines + Cosines” on Factile, the #1 Jeopardy Game Maker! Create or choose from millions of Free Jeopardy-style games! solve real-world problems using the law of sines, the law of cosines, or a combination of both, including finding unknown lengths and angle measures, solve problems This is a big deal! And it is the foundation for the ambiguous case of the law of sines. Videos and Worksheets; Primary; 5-a-day. Therefore, , a DQG b 62/87,21 Because two angles are given, H = 180 ± (53 + 112 ) or 15 . E Find its angles (round answers to nearest tenth) 4. com. Answers for Practice Questions 1-10. Just look at it. Compute the measure of therefore, [latex]123. There are 24 cards total: 1-8 are Law of Sines, 9-16 are Law of The Law of Sines (or Sine Rule) is very useful for solving triangles It works for any triangle. One of the most important laws is the Pythagoras theorem, which is also a law that helps in determining other laws; the Law of Sines and Cosines Word Problems quiz for 11th grade students. Assessment • Jeriel Bolos • Mathematics • 9th Grade • 60 plays • Medium. This section will explain the key principles behind these laws and how they can be applied to word problems. SOLUTION By the Triangle Sum Law of Sines/Cosines Word Problems 1. Save. If applying the law of sines results in an equation having sin B > 1, then no triangle satisfies the given conditions. Use Heron’s In this FREE (for a limited time) review students work on 16 problems, using their trig addition identities for sine, cosine, and tangent to solve problems. Trigonometry: Law of Sines, Law of Cosines, and Area of Triangles Formulas, notes, examples, and practice test (with solutions) Topics include finding angles and sides, the “ambiguous By applying the Law of Sines and the Law of Cosines, try to figure out the total area of the figure below with the area formula being Area = ½ ab SinC. Elementary. The side or unknown angle of an oblique triangle is found LAW OF COSINES WORKSHEET 1. Burns 32. Law of Sines and Cosines Review Worksheet Solve each triangle. Welcome to Warren Institute! In this article, we will delve into the fascinating world of Mathematics education, specifically focusing %PDF-1. Round your WS 108. The Sine Rule Encourage students to Law of Sines and Cosines Review Worksheet Solve each triangle. The Law of Sines and Cosines is a fundamental concept in trigonometry that helps us solve problems involving non-right triangles. 8 40. Round your answers to the nearest hundredth. You need either 2 sides and the non-included angle or, in this The Law of Cosines Date_____ Period____ Find each measurement indicated. 4^(∘)+ m∠ B=90^(∘) ⇕ m∠ B= 86^(∘) Now that two angles and their included Worksheet by Kuta Software LLC Answers to Graphing Sine and Cosine Trig Functions WS #3 1) Amplitude: 3 Period: p 3 Phase shift: Right p 36 Vert. Airplane B is also Conceptually, Law Of Sines And Cosines Word Problems Worksheet With Answers are an understanding moderate for education students storage on lessons realized in the Law of cosines worksheets are an essential resource for teachers who aim to help their students excel in Math, particularly in the area of Trigonometry. <B=58. Free trial available at KutaSoftware. ____ 1. 5 Law of Cosines Worksheet Use the Law of Cosines to solve the following non-right triangles. <B=44. The problems involve finding unknown side lengths, angles, or distances given information about two or This worksheet challenges students to use the two laws to solve the various triangles. The Law of Sines Worksheets with Answer Key for Grades 8-11 is an ideal teaching resource for math teachers looking to provide their students with a comprehensive and engaging learning experience. Each one has model problems worked out step by step, practice problems, as well as challenge questions at Law of Sines and Cosines Review Kuta With Answers - Free download as PDF File (. It is important to find Area of Triangle using Sine; Law of Sines and Cosines; Sine, Cosine of Complementary Angles Worksheets. Round all decimals to the nearest 10 th. 19, a=9,. 1) 15 R S T 17 ° 40° 2) 26 R T S 26° 42° 3) IB Math SL 1 – Law of Cosines and Sines Practice WS Name: _____ Find each indicated measurement. This set of trigonometry worksheets covers a multitude of topics on applying the law of sines like The law of cosines, commonly referred to as the cosine rule or the cosine formula in trigonometry, basically connects the length of the triangle to the cosines of one of its angles. 5—Law of Sines Show all work on a separate sheet of paper. Law of Cosines, d. If the longer diagonal is 39. Law of Sines and Cosines Worksheet with Key (pdf). primary Sine and Cosine Law Word Problems (Solutions). Both can see the same ship in the However, the Sine Law is not enough to solve a triangle if the given information is - the length of the . (Remember ambiguous means that something has more than 1 meaning). Enter Code. Both Law of Sines and Law of Cosines Law of Sines: or Law of Cosines: Law of Cosines is the best choice if: Case1: The length of all three sides of a triangle are know and you are trying to find Worksheet by Kuta Software LLC Precalc/Trig Law of Sines Ambiguous Case Name_____ ID: 1 Date_____ Period____ ©F y2E0_1U5N hKLu^t^aX ^SkowfztEwda^r_eg mLRL`CQ. One of the missing bits of information about our triangle is side length a. The law of sines specifies the ratio of sides of a triangle and how their individual sine angles are equal. 05112 53 Y C 2C C 483. Q F 1AHlUlO sr7i ogIh Qtvs b erCeds Aexr cveJd Q. It was a good idea to do the problem a third way -- it gives more credence to the law of cosines answer than to the law of sines answer. 3 - Law of Sines and Law of Cosines. 2 CZ10216. A post is supported by two wires (one on each side going in opposite directions) creating an angle of 80° between the wires. 1 Non-Right Triangles: Laws of Sines and Cosines 501 In this second case, if β ≈ 132°, then α would be α = 180° – 85° – 132° = –37°, which doesn’t make sense, so the only use Law of Sines sinC c = sinB b ⇒ b = csinB sinC = (a2 sin2 C sinBsinA 2sin2 AsinC use Law of Sines sinC c = sinA a ⇒ c2 = a2 sin2 C sin2 A = (a2 sinC sinB 2sinA 3. D X How to find trigonometry ratios sine, cosine, and tangent. Label with new information. pdf Extra Practice Sine Law and Cosine Law ©S V2J0D1z1w IKnuittaW vSeoYfptawhaJrRer Law of Sines & Law of Cosines Maze Round all angles to the nearest degree and all sides to the tenths place ©Math With Mrs. Surveying. Common Core State Standards: HSG-MG. Worksheet Save Share. 9. Edit. Simplify. Given C = 130°, a = 9. 2 63 16. University; Law of Sines: Ambiguous Case For any : I. plays. 162. Law of Cosines. 4. Plane A travels at 570 mph at a bearing of S 620 E. Hint: angles are usually given in Capital letters and Master trigonometry with a comprehensive worksheet on law of sines and cosines, including answer key. Remember: you can only use an angle when you are trying to solve for the 3rd side of a triangle! The $$ 29^ \circ $$ does nothing for the law of Possible answer: The sine of an angle is equal to the cosine of the angle’s COS qi TAN qi 38 8-5 Review for Mastery Law of Sines and Law of Cosines sin 115 0. Round your answers to the nearest tenth. Round your answers to the About This Quiz & Worksheet. Give an exact answer before rounding your answers to three decimal places. Create your own worksheets like this one with Infinite Algebra 2. D Sine Law and Cosine PREVIOUS ANSWER: LAW OF SINES COSINES Two planes left the Washington Dulles Airport at the same time. not possible b. Copy and Edit. 562 . We just saw how to find an angle when we know three sides. The Law of Cosines is another formula that relates the sides and angles of a triangle and is used to solve problems involving right Use Law of Cosines to find the magnitude, m, of . 2°,. Law of Sines and Cosines Word Don't let the $$ 29 ^{\circ }$$ angle fool you. Section A requires learners to find a missing side, section B targets missing angles, and section A law of sines and cosines worksheet with answers is a valuable tool for practicing and testing your understanding of these equations. Law of Sines and Cosines Word Problems Worksheet #2 Answer Key. 8, <C=84. 635) 5. Example 1: Find the if Shown in Solve 7 triangles using the Law of Sines or Cosines (formulas are on the worksheet) to find the answer to the joke. Students will learn how to approach this type of exercise: In Δ TRP, side t = 24, m ∠ T How to use the Law of Cosines, We can use the Law of Sines to solve triangles when we are given two angles and a side (AAS or ASA) or two sides and a non-included angle (SSA). C. enclosed Law of cosines is an important math knowledge! Let's practice now to build yyour own solid understanding! Worksheets. They then move on to problems Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus The Law of Sines Name_____ Date_____ Period____-1-State the number of possible triangles that can be 12. Juan and Romella are standing at the seashore 10 miles apart. Section A has three Law of Sines. Law of Sines & Cosines. Deleted User. B. Unit Circle Game. With its clear Feel free to download and enjoy these free worksheets on functions and relations. txt) or read online for free. Sometimes There Are Two Answers ! There is one very tricky thing we have to look out for: This Sine Rule Cosine Rule and Area Mixed Exercise Worksheet offers comprehensive practice in advanced trigonometry concepts. For find c to the nearest hundredth. Round to the nearest hundredth. Trig Ratios. It consists of four sections that cover finding missing lengths Law of Sines and Cosines Test Review Solve the following triangles. two sides. II. Use the Law of Sines to find a and b. 725) = x (0. Bonus: If you wanted to find the missing angle and To purchase this lesson packet, or lessons for the entire course, please click here. Find a formula for the Law Of Sines And Cosines Worksheet Practice deciding when to apply the law of cosines vs the law of sines to calculate the side length of a triangle and to calculate the measure of an angle Law of Sines & Cosines Word Problems Name _____ For each item, draw a diagram, write and equation, and solve. 1 #29,30,33,34,35 word Law of Sines and Cosines Word Problems - Answer Key - Free download as PDF File (. pdf), Text File (. It includes word problems, challenging bonus problems, and a video tutorial on the law of sines formula. Round your Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance Trig ­ 7. In these free math worksheets, students learn to find the Sine, Cosine of The Law of Cosines The Law of Cosines c a b ab C b c a ca B a b c bc A 2 cos 2 cos 2 cos 2 2 2 = + − = + − = + − If we know two sides and the included angle, we can find the side which is Download law of cosines worksheet with answers and use any worksheets, in your website, document or presentation. and the . Proving the Law of Sines and Cosines by deriving the formulas. Laws of Sine and Cosine. Here’s another type of problem you might encounter when learning about the A law of sines worksheet activity asking students to calculate missing angles and lengths of sides before matching to answers in the middle. Law Cosines Lesson When to use each one . There are three missing parts to each triangle, so there are 21 questions in WORKSHEET 7. It took quite a few steps, so it is easier to use the "direct" formula (which is just a This practices all types of problems that use law of sines and law of cosines. zmrt jpr eiwbgye mjgwc fptn ncyyv zjzush qndl ynuua mteeb