Question

Can someone explain this to me please?

Answer 1

Option C

Explanation:

Since, measure of all sides of the triangle has been given in the picture,

By applying cosine rule in the given triangle,

AC² = AB² + BC² - 2(AB)(BC)cos(B)

11² = 16² + 16² - 2(16)(16)cos(B)

121 = 256 + 256 - 512.cos(B)

121 - 512 = - 512.cos(B)

cos(B) =
`(391)/(512)` = 0.763672

B =
`cos^(-1)(0.763672)`

B = 40.2°

Therefore, measure of angle B is 40.2°.

Option C is the answer.