How to solve the height of the building of this math question?

Question

The angle of elevation to the top of a building in New York is found to be 9 degrees from the ground at a distance of 1 mile from the base of the building.

What is the formula? and how to solve the height of the building?

Answer 1

If you draw the triangle, 1 mile is adjacent, and the angle is 9°, so the height is 1 mile tan 9° = .158384 miles =

.158384 miles (5280 ft/mile) = 836.27 ft.

Answer 2

We can use tangent = O/A = opposite/adjacent = Height of building / distance from building

1 mile = 5280 feet (so height also in feet)

Hence tan (9 deg) = H / 5280

=> H = 5280 tan (9 deg) = 836 feet (to nearest foot)