Question

To prepare for a triathlon, Amanda starts from position A and rides her bike along a straight road for 12 miles to reach position B. At B, she turns left and rides along another straight road for 15 miles to reach position C. At C, she turns left again and rides 20 miles along a straight road to return to A. In ΔABC, what are m∠A, m∠B, and m∠C, respectively?

Answer 1

48.35°, 94.94°, 36.71°

Answer 2

The angles can solved by using the cosine law. Solving for the measure of angle A
15² = 20² + 12² - 2(20)(12) cos A
A = 48.35°

Angle B can solved by either also using the cosine law or by sine law. Let's use sine law:
20 / sin B = 15 / sin 48.35
B = 85.06°

The measure of angle C can just be solved by difference of the total angle of the triangle.
C = 180 - 48.35 - 85.06
C = 45.59°