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
