So first off lets label the sides.
line XY is adjecent to the angle we want to find out
Line YZ is the hypotenuse
If we remember SOH CAH TOA
Then we know we use cos because we know the adjacent side and the hypotenuse. It also tells us that we divide the adjacent side by the hypotenuse.
Lets do this
cos(x) = adj / hyp
cos(x) = 6 / 15
x = cos^-1 (6 / 15)
x = 66.4
So angle XYZ = 66.4 degrees
The next one is very similar. Label the sides again.
line YZ is still the hypotenuse
but line XY is now opposite the angle we want.
If we remember SOH CAH TOA
We know that we use sin because we know the opposite and the hypotenuse. We also know to divide the opposite by the hypotenuse
sin(x) = opp / hyp
sin(x) = 6 / 15
x = sin-^-1 (6/15)
x = 23.6
So angle XZY = 23.6 degrees