Question

Find the measure of angle B. Show work please​

Answer 1

C 54.6°

Explanation:

Using cosine law:

18² = 10.4² + 21.9² - 2(10.4)(21.9)cosB

cosB = 2029/3504

B =54.6160711

Answer 2

c. 54.6°

Explanation:

The Law of Cosines can be used to find the first of the unknown angles in a triangle with only three side lengths given.

b² = a² +c² -2ac·cos(B)

Solving for B, we have ...

2ac·cos(B) = a² +c² -b²

B = arccos((a² +c² -b²)/(2ac)) = arccos((10.4² +21.9² -18²)/(2(10.4)(21.9)))

B = arccos(0.579053) ≈ 54.6° . . . . . matches choice C