The Law of Cosines

Question 8Given b = 12, c = 20, and A = (/4), Manipulate the formula to solve for a.

A. sqrt(144+400-480cos(/4))B. sqrt(144+400-480cos(45))C. A. and B. are the same answerNO, TRY AGAIN.Throw your numbers into yourcalculator, using the formulasgiven earlier in the presentation.

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InformationFormulasa2 = b2 + c2 2bc(cos(A))b2 = a2 + c2 2ac(cos(B))c2 = a2 + b2 2ab(cos(C))

Example 1Given a triangle with side measures, a = 4, b = 5, and c = 7, Solve for the angles (NOTE: Angles are measured in degrees).

A. A = 34.0, B = 44.4, C = 101.6B. A = 0.60, B = 0.80, C = 178.6C. A = 0.8, B = 0.7, C = 178.5QuizThere is no time limit. However, you must pass this quiz with 100% accuracy. You may take this quiz as many times as you wish. Good Luck!Extra Helpful Videoshttp://www.youtube.com/watch?v=QkpDJaze31khttp://www.youtube.com/watch?v=FPmdo1xiMDYhttp://www.youtube.com/watch?v=WRsAQpFoEg0

Please use these links if you are having trouble accessing the embedded videos on this PowerPoint.

If there is an issue with viewing the videos on this PowerPoint, then please use these links. Thank you.http://www.youtube.com/watch?v=hfPIw9WfpmQhttp://www.youtube.com/watch?v=4Bfk6Wc9vNM&context=C41709ffADvjVQa1PpcFNBdTOOCAoTJc1fS0NQ5YddXCQ0wuD5yyc=

Formulas (cont.)cos A = (b2 + c2 a2) / (2bc)cos B = (a2 - b2 + c2) / (2ac)cos C = (a2 + b2 - c2) / (2ab)

NOTEOnce you find two angles, sum them and then take 180 and subtract the sum of the two angles that you have.In addition, lower-case letters represent side measures, and upper-case for angle measures.In Slides 17 and 18, you may click on the image in the middle of the page that will take you to an example problem.

ApplicationThere are two cases in which the Law of Cosines can be used.

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Let us take a look at some example problems. When you answer a question correctly, please click the triangle on the left-hand side of the correct answer slide for a solution.Question 1Triangle ABC with side measures, a = 9, b = 12, c = 13.5. Solve for the angle measures.

A. A = 40.8, B = 60.6, C = 78.6B. A = 1.18, B = 1.06, C = 177.76

Referencesmathworld.wolfram.com/LawofCosines.htmlpublic.asu.edu/~kamman/notes/trigonometry/Law-of-Cosines-r10-14-2007.htmlkkuniyuk.com/M1410602.pdfmathproofs.blogspot.com/2006/06/law-of-cosines.htmlregentsprep.org/Regents/math/algtrig/ATT12/lawcosinespractice.htmwww.youtube.com/watch?v=FPmdolxiMDYwww.youtube.com/watch?v=paDc0Mdw48www.youtube.com/watch?v=QkpDJaze311cwww.brightstorm.com/math/trigonometry/basic-trigonometry/the-law-of-cosineshttp://images.all-free-download.com/images/graphiclarge/ok_mark_clip_art_9019.jpghttp://static.fjcdn.com/comments/WRONG.+wolverine+is+a+mutant+not+an+experiment+_73eea773f3d6e739ba800a3317929694.pnghttp://www.coursehero.com/tutors-problems/Math/6450857-To-approximate-the-length-of-a-lake-a-surveyor-starts-at-one-end-of-t/ (Word Problem in Video)

NOTE: The answer is NOT present in the site.

Ahh, Young Padawan, you are ready to take on the world of trigonometry.