Answer:
Height = 64 feet
Explanation:
(***It's very important to model these kinds of problems. I attached a picture modeling the problem so show how modeling makes it easier to solve the problem)
We know that the building is vertical, and the ground is horizontal. Thus, the ground and the building make a right angle.
Therefore, the top of the building, the base of the building, and the surveyor form a right triangle, where
- The distance between the surveyor and the building is a leg of the triangle,
- The height, h of the building (aka distance between the top of the building and the base) is another leg of the triangle,
- and the distance between the top of the building and the surveyor is the hypotenuse.
Because we're working with a right triangle, we can now find h, the heigh of the building using one of the trigonometric ratios.
We know that the angle of elevation is made by the ground and the distance between the surveyor and top of the building.
When the 65° (angle of elevation) is our reference angle, the height of the building is the opposite side and the distance between the base of the building and the surveyor is the adjacent side.
Thus, we can use the tangent ratio, which is: tan (θ) = opposite / adjacent:
We can now plug in 65 for θ and 30 for the adjacent side. This will allow us to find the opposite side, which is the heigh of the building:
tan (65) = h / 30
30 * tan(65) = h
64.33520762
64 = h
Thus, the height of the building to the nearest foot is 64 feet.