1. Advanced Geometry
Trigonometry
Lesson 5
The Law of Cosines

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

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

4. Example: Find m∠L to the nearest tenth.

5. 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

6. 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.

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