An observer, standing on level ground, 100 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.7 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.
A) h = 84.2 feet
B) h = 96.7 feet
C) h = 102.5 feet
D) h = 108.3 feet

Question

Quizplus · Accepted Answer

To find the height of the tower, we use the tangent of the angle of elevation, which is the ratio of the opposite side (height of the tower, h) to the adjacent side (distance from the observer to the tower, 100 feet). So, tan(0.7) = h / 100. Solving for h gives h = 100 * tan(0.7) ≈ 84.2 feet.

An Observer, Standing on Level Ground, 100 Feet from the Bottom