Question

Find the measure of the indicated angle to the nearest degree

Answer 1

You can use the sine law, which states that, in every triangle, the ratio between a side and the sine of the opposite angle is constant.

So, we have

$\dfrac{59}{\sin(90)}=\dfrac{42}{\sin(x)}$

where $x$ is the angle you're looking for. Now, remember that $\sin(90)=1$, and we can solve the equation for $\sin(x)$:

$\sin(x)=\dfrac{42}{59}$

Which implies that the angle itself is

$x=\arcsin\left(\dfrac{42}{59}\right)\approx 45.39$