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?

Hello there.

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?

m∠A = 48°

m∠B = 95°

m∠C = 37°

In ΔABC, we have the following lengths of the sides

AB = 12 mi

BC = 15 mi

CA = 20 mi

Using the cosine law to solve for the angles:

15 ² = 12² + 20² - 2 (12) (20) cos m∠A

20² = 12² + 15² - 2 (12) (15) cos m∠B

12² = 15² + 20² - 2 (15) (20) cos m∠C

m∠A = 48°

m∠B = 95°

m∠C = 37°