Hi, me with this maths. both questions . they are both small.

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

No he does not because he can only cover 12 square feet from 15 square feet which he will still need 3 more. this is because if 3×5=15 square feet and 15-12=3 which thats the answer