Question

Quick!!

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.

Answer 1

154 ft

Explanation:

tan64° =
`(h)/(75ft)`

h = tan64° * (75ft)

h = 2.0503038416 * 75

h = 153.77278812 ft or 154 ft rounded to the nearest foot

Answer 2

The height of the building is approximately;

B. 154 ft

Explanation:

From the given drawing of the right triangle formed by the measure of the angle to the top of the building, 64°, the height of the building, 'h', and their distance from the bottom of the building, 75 ft., we have;

The reference angle of the right triangle = The given 64° angle

The adjacent leg length to the reference angle = 75 ft.

The opposite leg length to the reference angle The height of the building

From the given information, the trigonometric ratio we can use to find the height is the tangent of the reference angle, given as follows;

`tan (Reference \, angle) = (Opposite \ leg \ length)/(Adjacent \ leg\ length)`

Therefore, we have;

`tan (64^(\circ)) = (The \ height \ of \ the \ building, h)/(75 \, ft.)`

The height of the building, h = 75 ft. × tan(64°) = 153 feet
`9(9)/(32)` inches

Therefore, the height of the building ≈ 154 feet.