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.
To the nearest foot, what is the height of the building?
150 ft
105 ft
32 ft
160 ft
To find the height of the building, we can use trigonometric functions. Let's consider the right triangle formed by the building, the ground, and the line of sight from the students' location to the top of the building.
We are given that the distance from the students to the building is 105 ft, and the angle from their location to the top of the building is 30 degrees. This angle is opposite the height of the building.
We can use the tangent function to find the height of the building:
tan(30°) = height / 105 ft
height = 105 ft * tan(30°)
height ≈ 61 ft
Therefore, the nearest height of the building to the nearest foot is 61 ft.