2 In triangle ABC AB10 BC 6 and the measure of angle A 30 Fi

2. In triangle ABC, AB-10, BC 6 and the measure of angle A- 30°. Find tan(C). (Hint: This triangle is not a right triangle. Draw a picture and include the altitude from vertex B to the side AC)

Solution

AB = 10 , c = 10

BC = 6 , a = 6

angle A = 30 degrees

applying law of sines

a / sin A = c / sin C

6 / sin 30 = 10 / sin C

12 = 10 / sin C

sin C = 10/12 = .83333

C = 56.44 degrees

tan C = 1.5074