the angle of elevation from the tip of the shadow of a 12ft flagpole to the top of the pole is 60 degrees. how far is it from the tip of the shadow to the top of the pole

Given b = 12 ft, B = 60° in a right triangle formed by the pole, its shadow, and the line connecting the tip of the shadow to the top of the pole (denote its length by c).

c = b / sin B = 12 / sin 60° = 12 / (sqrt{3} /2) = 24 / sqrt{3} = 8 sqrt{3} = 13.9 ft. .