Sometimes the hardest part is trying to figure out what's going on. Draw a picture and things fall in place:

Looking only at the big triangle (top of billboard):

You can calculate θ by saying tan(θ) = 60/25 so θ = tan^{-1}(60/25) = 67.38°

Since the smaller angle (to the top of the base) is 1/2θ, then it is 67.38°/2 = 33.69°

Now, using the smaller triangle (top of base):

You can now say tan(33.69) = x/25 or x = 16 2/3 ft (≈ 16.67 ft)

The billboard is 60 - 16 2/3 = 43 1/3 ft (≈ 43.33 ft)