1 What you will learn  How to solve triangles by using the Law of Cosines  How to find the area of triangles if the measures of the three sides are given

Objective: 5-8 The Law of Cosines 2 Law of Cosines When given three side lengths (SSS) or two sides and the included angle (SAS), the law of sines won’t work. For these situations, we have the law of cosines. a 2 = b 2 + c 2 – 2bc cos A b 2 = a 2 + c 2 – 2ac cos B c 2 = a 2 + b 2 – 2ab cos C

Objective: 5-8 The Law of Cosines 3 Example for SAS  Solve the triangle: A = 120 o, b = 9, c = 5 Use: a 2 = b 2 + c 2 – 2bc cosA because A and not a.

Objective: 5-8 The Law of Cosines 4 You Try  Solve the triangle: A = 39.4 o, b = 12, c = 14

Objective: 5-8 The Law of Cosines 5 Another Example SSS  Solve the triangle: a = 24, b = 40, c = 18. Angle B is the largest. How do you know? Use b 2 = a 2 + c 2 – 2ac cosB

Objective: 5-8 The Law of Cosines 6 You Try  Solve the triangle: a = 19, b = 24.3, c = 21.8

Objective: 5-8 The Law of Cosines 7 Finding Area – SSS  Find the area of triangle ABC if a = 4, b = 7, and c = 9.  Find angle A then use

Objective: 5-8 The Law of Cosines 8 Finding Area – Hero’s Formula  If you know three sides of a triangle and no angle measures, you can use Hero’s Formula to calculate area:

Objective: 5-8 The Law of Cosines 9 Example of Hero’s Formula  Find the area of triangle ABC with a = 72, b = 83, and c = 95.

Objective: 5-8 The Law of Cosines 10 You Try  Find the area of ABC with a = 47, b = 53, and c = 44.

Objective: 5-8 The Law of Cosines 11 Homework  page 331, odd, 25, 28