You did both correctly.
For the first part, you can figure out most if it using only geometry. A right triangle with two equal sides is a 45-45-90 triangle. A right triangle with sides is a 30-60-90 triangle (where is the 30 degree angle). So, . This means .
You get the same answer either way.
I was taught that the sides of a 30-60-90 triangle will have lengths where is the length of the side opposite the 30 degree angle, is the length of the side opposite the 60 degree angle, and is the length of the hypotenuse in geometry class. I assumed it was still taught. As for the other angle, convert degrees to radians: .
I calculated mine using vector product: . It's also possible to use dot product to find cosine first. If the angles are arbitrary, I would guess the problem authors' intention was to use the formula
The values in the right-hand side can be found by definition.