If the angle from the horizontal to the top of a building is $34 ^ { \circ }$ and the horizontal distance from the base is $91$ ft, what is the height of the building (to the nearest foot)?
A) 61 ft
B) 135 ft
C) 163 ft
D) 75 ft
E) 51 ft

Question

Quizplus · Accepted Answer

The height of the building can be found using the tangent function in trigonometry, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 34^\circ$ and the adjacent side (the horizontal distance) is 91 ft. So, the height of the building (opposite side) is $\tan(34^\circ) \times 91$. Calculating this gives a height of approximately 61 ft, rounding to the nearest foot.

If the Angle from the Horizontal to the Top of a Building