First notice that angle C is a right angle, then:

Now, since this is a right triangle, we can find the measure of angle A using the trigonometric function sine:

In this case, we have the following:

Since the sum of the interior angles of a triangle equals 180, we can find the measure of angle B by solving the following equation:

therefore, angle A measures 48.6 degrees and angle B measures 41.4 degrees