Advanced Geometry Trigonometry Lesson 5 The Law of Cosines

Derive the Law of Cosines b b c c x B B C C a - y y a a The Law of Cosines

Example: Find x if y = 11, z = 25, and m∠X = 45. Round to the nearest tenth.

Example: Find m∠L to the nearest tenth.

When solving a triangle, you must decide which method to use. If you are given … begin by using… two angles and any side Law of Sines two sides and the angle opposite one of them Law of Sines two sides and the included angle Law of Cosines three sides Law of Cosines

Example: Determine whether the Law of Sines or Law of Cosines should be used first to solve ∆DEF. Then solve ∆DEF. Round angle measures to the nearest degree and side measures to the nearest tenth.

Example: Solve ∆XYZ for x = 10, y = 11, and z = 12. Round measures to the nearest tenth.