Question

15. What is x to the nearest tenth?

А
2
62
44
C.c

B
78
A 37.5
B 52.5
© 75.0
D 103.0

Answer 1

................

D 103.0

Answer 2

The nearest tenth options closest one is: A

To find the measure of angle B in the triangle, you can use the Law of Cosines,

`c^2 = a^2 + b^2 - 2ab cos(C).`

`a = AB = 44, b = BC = 78` and
`AC =62`

let C be the angle B.

`62^2 = 44^2 + 78^2 - 2 * 44 * 78 * cos(B).`

Now, solve for cos(B):

`cos(B) = (62^2 - 44^2 - 78^2) / (-2 * 44 * 78)`

`B = cos^(-1)((62^2 - 44^2 - 78^2) / (-2 * 44 * 78))`

The angle B and round to the nearest tenth.

`B = cos^(-1)((-5176) / (-6864))`

`B = cos^(-1)(0.754))`

B ≈ 41.6°.

Therefore, the nearest tenth is B ≈ 41.6 °, options closest one is: (A) 37.5.