Question

Find the measure of the indicated angle to the nearest degree

does anyone know the answer ?? Please help !

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

`(59)/(\sin(90))=(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)=(42)/(59)`

Which implies that the angle itself is

`x=\arcsin\left((42)/(59)\right)\approx 45.39`