The angle of elevation to the top of a very tall Building is found to be 7° from the ground at a distance of 1 mi from the base of the building.

Question

The angle of elevation to the top of a very tall Building is found to be 7° from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the building. (Round your answer to the nearest foot.)

Answer 1

If you imagine this graphically, the picture would appear that the building is the height of a right triangle. We will call this height x, since it is unknown. The base of this right triangle would be the distance from the bottom of the building to a point opposite the building. This distance is equal to one mile. The diagonal side of the triangle would connect the two points previously discussed. The angle nearest to the ground and inside that right triangle would be the angle of elevation.

Now that we have this mental image of the scenario, we can use trigonometry to solve the problem for the unknown value, the height of the building.

Knowing that the trigonometric function tangent is equal to the opposite over the adjacent side of a right triangle and substituting x for the unknown building height, we can write the following equation:

tan(7°) = x/1 mi.

After rearranging this equation to solve for x, we get x = (1 mi)*(tan(7°)) = 0.12278 miles

This means that the building height is 0.122 mi tall.