The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance.

Question

To the nearest foot, what is the height of the building? (1 point)

Responses

105 ft

116 ft

32 ft

54 ft

Answer 1

To find the height of the building, you can use trigonometry.

Given:
Angle measure = 32 degrees
Distance from the building = 54 feet

Let h be the height of the building.

Using the tangent function:
tan(32 degrees) = h / 54 feet
h = 54 feet * tan(32 degrees)
h ≈ 32 feet

Therefore, to the nearest foot, the height of the building is 32 ft.

So, the answer is 32 ft.