Question

In triangle ABC, a = 4, b = 7, and c = 10. Find A.
18°
34°
56°
162°

Answer 1

18°

Explanation:

The law of cosines tells you ...

a² = b² + c² -2bc·cos(A)

Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.

cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140

A = arccos(133/140) ≈ 18.2° ≈ 18°