Sighting the top of a building, a surveyor measured the angle of elevation to be 60°. The measurement is taken 200 feet from the building. Find the building’s height. Express your answer in terms of feet and then round to two decimal places

h/200 = tan 60°

To find the height of the building, we need to use trigonometry. Let's use the tangent function.

In this case, the angle of elevation (60°) represents the angle between the ground and the line of sight from the surveyor to the top of the building. The adjacent side is the distance from the surveyor to the building (200 feet), and the opposite side is the height of the building (which we need to find).

First, let's set up the equation using the tangent function:

tan(angle) = opposite / adjacent

Plugging in the values we know:

tan(60°) = opposite / 200

Now, let's solve for the opposite side (the height of the building):

opposite = tan(60°) * 200

Using a scientific calculator or a trigonometric table, we can find that tan(60°) is approximately 1.732.

opposite = 1.732 * 200

opposite = 346.4

Therefore, the height of the building is approximately 346.4 feet. Rounded to two decimal places, the height is 346.40 feet.