In triangle ABC, a = 3, b = 5, and c = 7. find the measure of B.

Solution:

Let's find the measure of ∠B.

Explanation:

Given a = 3, b = 5, and c = 7.

To find the measure of angle B, we will use Law of Cosine.

Substitute these values in the formula of law of cosines,

⇒ b² = c² + a² - 2ca cos B

⇒ 5² = 7² + 3² - 2 ( 7 × 3) cos B

⇒ 25 = 49 + 9 - 2 (21) cos B

⇒ 25 = 58 - 42 cos B

⇒ 42 cos B = 58 - 25

⇒ 42 cos B = 33

⇒ cos B = 33 / 42

⇒ B = cos^-1 33 / 42

⇒ B = cos^-1 (0.7856)

⇒ B = 38. 22º

Therefore, the measure of B is 38.22º.

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In triangle ABC, a = 3, b = 5, and c = 7. find the measure of B.

Summary:

In triangle ABC, a = 3, b = 5, and c = 7. The measure of B is 38.22º.