9-3

9-3 Law of Sines

We use Law of Sines on non-right triangles. You can use this formula when the triangle gives you an angle an opposite leg to solve the triangle. You will get two answers when you find the inverse. You cross multiply using the following formula:
sin A/a = sin B/b = sin C/c

Example 1: Triangle ABC gives you Angle A = 60, Angle B = 95, Angle C = 25, and a = 8. Solve the triangle.

• sin 60/8 = sin 25/c


• c sin 60 = 8 sin 25


• c = 8 sin 25/sin 60


• c = 3.904


• sin 95/b = sin 60/8


• b sin 60 = 8 sin 95


• b = 8 sin 95/sin 60


• b = 9.202


• 180 - 90 - 60 = 25


• Angle C = 25

Example 2: Triangle ABC gives you Angle A = 76, a = 12, and b = 4. Solve the triangle.

• sin 76/12 = sin B/4


• 12 sin B = 4 sin 76


• B = sin^-1 (4 sin 76/12)


• Angle B = 18.871


• 180 - 18.871 - 76 = 85.129


• Angle C = 85.129


• sin 76/12 = sin 85.129/c


• c sin 76 = 12 sin 85.129


• c = 12 sin 85.129/sin 76


• c = 12.323