Question

In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A. 22° 38° 142° 158°

Answer 1

Answer: 22 degrees

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Explanation:

Use the law of cosines to isolate angle A

a^2 = b^2 + c^2 - 2*b*c*cos(A)

3^2 = 5^2 + 7^2 - 2*5*7*cos(A) ... plug in a=3, b=5, c=7

9 = 25 + 49 - 70*cos(A)

9 = 74 - 70*cos(A)

74 - 70*cos(A) = 9

-70*cos(A) = 9 - 74 .... subtract 74 from both sides

-70*cos(A) = -65

cos(A) = -65/(-70) ... divide both sides by 70

cos(A) = 13/14

A = arccos(13/14) .... apply the arcosine function to both sides

A = 21.7867892982619

This rounds to 22 degrees