The angle of elevation to the top of a tall building is found to be 12° from the ground at a distance of 1.1 mile from the base of the building.

Question

Using this information, find the height of the building.

The buildings height is ____ feet.

Report answer accurate to 2 decimal places.

Answer 1

Drawing a sketch, the height of the building is the opposite side, x. The dimension given, 1.1 miles is the adjacent side. Therefore, we should use tan

tan Θ = opposite/adjacent. Plugging in values we know

tan 12 = x/1.1 Multiply both sides by 1.1

x = 0.2338 miles x 5280 ft/mile = 1227.51 ft