When you have a notable result, as 0, 1, 1/2, (√3)/2, you can deduce the angle from your own knnowledge. For example, the angles whose sin is 0 is 0° and 180°.
In cases of not notable sines, like the one of this problem, you need to use a table of trigonometric functions or a calculator with the function arctan (which is the inverse of the tangent, and sometimes written as tan^-1).
With a calculator I found arctan(0.39581) = 29.59°.
Now take in account that the function sine is periodic and this value is repeated when the angle is 180° - 29.59° = 158.41 °.
Answer: 29.59° and 158.41°.
