Question

Given the triangle below, what is mB, rounded to the nearest tenth?

Answer 1

Option D. 82.8°

Explanation:

From the figure attached,

By using Cosine rule in the given triangle ABC,

AC² = AB² + BC ² - 2(AB)(BC)cosB

(12)² = (8)² + (10)² - 2(8)(10)cosB

144 = 64 + 100 - 160.(cosB)

144 = 164 - 160.(cosB)

160.(cosB) = 164 - 144

cosB =
`(20)/(160)`

cosB =
`(1)/(8)`

B =
`\text{cos}^(-1)(0.125)`

B = 82.82°

B ≈ 82.8°

Therefore, Option D. will be the answer.