I've drawn a diagram to help.
In the diagram, the side of the right triangle we're looking for is across from, or opposite, our 64° angle. The 150 ft long string makes the hypotenuse of the right triangle formed. Opposite/hypotenuse is the ratio for sine, so we set up the following equation:
sin 64 = x/150
Multiplying by 150 on both sides to cancel it, we have
150 sin 64 = x
This comes out to 138 feet above the ground.
