Question

In the triangle shown below, what are the measures of angles A, B, and C? Round your answers to the nearest tenth of a degree. Show your work. You'll need to use a calculator to find the angles, LaTeX: \cos^{-1}cos − 1( ).

Answer 1

The answer to your question is

A = 29.6°

B = 115.4°

C = 35°

Explanation:

Process

1.- Use the Cosines law to answer this question

c² = a² + b² - 2abcosФ

Solve for cos Ф

cos Ф = (c² - a² - b² )/ -2ab

Substitution

cosФ = (7² - 6² - 11²) / (-2)(6)(11)

cosФ = (49 - 36 - 121) / -132

cos Ф = -108 / -132

cos Ф = 0.818

Ф = 35° = C

Find B

cos Ф = (b² - a² - c²) / (-2ac)

cos Ф = (11² - 6² - 7²) / (-2)(6)(7)

cos Ф = ( 121 - 36 - 49) / -84

cos Ф = 36 / -84

cos Ф = -0.429

Ф = 115.4° = B

2.- Find a

The sum of the internal angles in a triangle equals 180°

A + B + C = 180

A + 115.4 + 35 = 180

A = 180 - 115.4 - 35

A = 29.6°