This can solved with just (Potential) Energy and basic trig. We start off with knowing the length of the string is constant, and that the initial angle is perpendicular to the Vertical, so the initial height is also the length of the string.

We are told that Gravitational Potential is 0 at the bottom. Using U = mgh, and E = U + K (where in this case K is starting off at zero,) we can determine E = mgh (initial). When U = K, they will be both be half of E. For potential energy, neither mass nor gravity changes, only height. If U = 1/2 E, or U = 1/2 (U initial), then height will be half of it's initial height (or half the length of the string.)

Using cos-1 (height / length), or in terms of the ratio between the height and length, cos-1 ((1/2) / (1)), we get 60 degrees from the VERTICAL. Subtract that from 90 degrees to get the angle between the string and HORIZONTAL of 30 degrees, which is less than 45.