Answer:
The height of the building is approximately;
B. 154 ft
Step-by-step 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;
[tex]tan (Reference \, angle) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg\ length}[/tex]
Therefore, we have;
[tex]tan (64^{\circ}) = \dfrac{The \ height \ of \ the \ building, h}{75 \, ft.}[/tex]
The height of the building, h = 75 ft. × tan(64°) = 153 feet [tex]9\dfrac{9}{32}[/tex] inches
Therefore, the height of the building ≈ 154 feet.
