Question

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

22°
38°
142°
158°

Answer 1

9514 1404 393

Answer:

a) 22°

Explanation:

Side 'a' is the shortest side, so angle A will be the smallest angle. Its value must be less than 60°, eliminating the last two answer choices. The actual value can be found from the Law of Cosines.

a² = b² +c² -2bc·cos(A)

cos(A) = (b² +c² -a²)/(2bc) = (5² +7² -3²)/(2(5)(7)) = 65/70

A = arccos(65/70) ≈ 21.7868°

Angle A is about 22°.