Question

The angle of elevation to the top of the Empire State Building in New York is found to be 11° from the ground at a distance of 5281 feet from the base of the building. Using this information, find the height of the Empire State Building in feet. Use the dimensions given in the diagram to give an equation and solve. Round two decimal places.

Answer 1

The height of the building is of 1026.52 feet.

Explanation:

This situation is modeled by a right triangle, in which the length of the opposite side to the angle of 11º is the height of the building, while the length of the adjacent side is of 5281 feet.

Tangent:

In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.

In this question:

`tan((11)) = (x)/(5281)`

`x = 5281*tan((11))`

Using a calculator, we have that the tangent of 11 degrees is: 0.1944. Thus:

`x = 5281*tan((11)) = 5281*0.1944 = 1026.52`

The height of the building is of 1026.52 feet.