find the height of the building

Question

The angle of elevation to the top of a Building in New York is found to be 7 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths.

Answer 1

The angle of elevation is an angle from a horizontal axis facing upward towards an object. One way to go about this problem is to draw it out as a right triangle, with the ground distance of 1 mile being the adjacent side to the 7^o angle and the building being the opposite side.

For right triangles, the tangent of an angle is in the length of the opposite side divided by that of the adjacent side.

We have the angle of elevation (7^o) and adjacent side (1 mile = 5280 ft), so we can use the tangent formula to solve for the opposite side, which is the height of the building. Make sure that you use degrees and not radians!

tan(α) = opposite/adjacent

tan(7^o) = x/(5280 ft)

x = (0.122784)(5280 ft)

x = 648.3 ft