Question

Use the triangle below to solve for the indicated angle.

Answer 1

$\angle x\approx39^{\circ},\angle y\approx51^{\circ}$

1) We were told to find the measure of each angle.

2) So, let's make use of some trig ratios. And let's find the measure of ∠x

$\begin{gathered} \sin (x)=\frac{5}{8} \\ (x)=\sin ^{-1}(\frac{5}{8}) \\ x=38.68^{\circ} \end{gathered}$

Notice that since we need to find the measure of the angle we had to resort to the arcsine of (5/8) to find that.

So, let's now, find the measure of ∠y

$\begin{gathered} \cos (y)=\frac{5}{8} \\ y=\cos ^{-1}(\frac{5}{8}) \\ y\approx51.32^{\circ} \end{gathered}$

So let's round them off to the nearest whole number. Then the answer is:

$\angle x\approx39^{\circ},\angle y\approx51^{\circ}$