From the base of a building, measure out a horizontal distance of 225 ft along the ground. The angle of elevation to the top of the building is 57.0 ^o. Find the height of the building. A) 338 ft B) 362 ft C) 366 ft D) 346 ft E) 319 ft

Question

Quizplus · Accepted Answer

The height of the building can be found using the tangent of the angle of elevation, which is the opposite side (height of the building) over the adjacent side (distance from the building). Using the formula $\tan(\theta) = \frac{opposite}{adjacent}$, where $\theta = 57^\circ$ and the adjacent side is 225 ft, we solve for the opposite side (height). $\tan(57^\circ) = \frac{height}{225}$, so $height = 225 \times \tan(57^\circ)$. Calculating this gives a height of approximately 346 ft.

From the Base of a Building, Measure Out a Horizontal