Explanation:
first, remember Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle).
a and b are the legs.
so, in our case
c² = 4² + 6² = 16 + 36 = 52
c = sqrt(52) = 7.211102551... ≈ 7.21
and then remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the corresponding opposite angles (here also called alpha, beta. gamma would be the 90° angle).
so,
4/sin(alpha) = c/sin(90) = c
4 = c×sin(alpha)
sin(alpha) = 4/c = 4/7.211102551... = 0.554700196...
alpha = 33.69006753...° ≈ 33.69°
we don't need to do that much calculation for the third angle beta, as we know the sum of all angles in a triangle is always 180°.
so,
180 = alpha + beta + 90 = 33.69 + beta + 90
90 = 33.69 + beta
56.30993247... = beta ≈ 56.31°