In triangle ABC, side b=15 units while side c=20 units. The measure of angle B is 43˚. If ABC is obtuse, what is the measure of angle C?

Question

This is an obtuse triangle. The subject is trigonometry.

Answer 1

This question can be solved using law of sines. Law of sines states

a/sinA = b/sinB = c/sinC

In this problem, we've been asked to solve for angle C. The problem can be set up in the following way:

b = 15

angle B = 43 degrees

c= 20

angle C = ?

Therefore, 15/sin43 = 20/sinC

We can cross multiply to come to

15*sin C = 20 * sin 43

20*sin 43 degrees = 13.64

Therefore, 15*sin C = 13.64

Dividing 15 from both sides, we get 0.91

Hence, sin C = 0.91

Angle C can now be derived using inverse sine on a calculator. We get 65.5 degrees or 66 degrees.