Question

See figure below. Round answer to the nearest tenth of a degree

Answer 1

ANSWER

$\begin{equation*} 109.2\degree \end{equation*}$

EXPLANATION

We want to find the measure of angle B.

To do this, we first have to find the measure of angle C using the sine rule:

$\frac{\sin C}{AB}=\frac{\sin A}{BC}$

Substitute the given values into the equation and solve for C:

$\begin{gathered} \sin C=\frac{AB*\sin A}{BC} \\ \\ \sin C=\frac{180*\sin42}{250} \\ \\ \sin C=\frac{120.4435}{250}=0.4818 \\ \\ C=\sin^{-1}(0.4818) \\ \\ C=28.8\degree \end{gathered}$

Now, we can find the measure of angle B using the sum of angles in a triangle. The sim of angles in a triangle is 180 degrees. This implies that:

[tex]\begin{gathered} That is the measure of angle B.