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

Given the triangle below, what is mB, rounded to the nearest tenth?-example-1

1 Answer

3 votes

Answer:

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.

User Rafalmag
by
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