In triangle ABC, a = 9, c = 5, and angle B = 120Á. Find the measure of angle A to the nearest degree. Show your work.

Question

Mathematics

Santos Powell

3 December, 12:12

In triangle ABC, a = 9, c = 5, and angle B = 120Á. Find the measure of angle A to the nearest degree. Show your work.

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Answers (1)

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Zayne Reilly · Answer 1

B = sqrt (a^2 + c^2 - 2ac cos B) = sqrt (9^2 + 5^2 - 2 x 9 x 5 x cos 120°) = sqrt (81 + 25 - 90cos120°) = sqrt (106 + 45) = sqrt (151) = 12.29

b/sin B = a / sin A

12.29/sin 120° = 9/sin A

sin A = 9sin 120° / 12.29 = 0.6343

A = arcsin (0.6343) = 39°