In triangle ABC, a = 9, c = 5, and B = 120°. Find b².

Solution:

Let us use the law of cosines

b² = a² + c² - 2ac cos B

Where the angle B is across from side b

It is given that

a = 9, c = 5, B = 120°

Substituting the values

b² = 9² + 5² - 2 (9) (5) cos (120°)

By further calculation

b² = 81 + 25 - 90 (-1/2)

So we get,

b² = 106 + 45

b² = 151

Therefore, b² is 151.

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In triangle ABC, a = 9, c = 5, and B = 120°. Find b².

Summary:

In triangle ABC, a = 9, c = 5, and B = 120°. b² = 151.