Verified answer

We are given Ux = U cos(theta) = 15 mps and Uy = U sin(theta) = 12 mps. So we have Uy/Ux = tan(theta) and theta = ATAN(Uy/Ux) = ATAN(.8) = 38.66265599 = 38.7 deg re the XX axis.

So we have U = Uy/sin(38.7) = 12/sin(radians(38.7)) = 19.19254849 = 19.2 mps @ theta = 38.7 deg re the XX when you need the vector. ANS.

The two vectors can be added tip to tail. They form a right angle triangle so we can use Pythagorus to find the resultant velocity (hypothenuse). I will assume you don't need to find the vector and that a scalar speed is sufficient.

Vres=√15.0^2+12.0^2

Vres=√369

Vres=19.2m/s