Question

question
from a hot-air balloon, brody measures a $32^\circ$ angle of depression to a landmark thats 1081 feet away, measuring horizontally. whats the balloons vertical distance above the ground? round your answer to the nearest tenth of a foot if necessary.
answer
attempt 1 out of 2
feet

Explanation:

Step1: Define trigonometric relation

The angle of depression equals the angle of elevation from the landmark to the balloon. We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=32^\circ$, opposite side is vertical distance $x$, adjacent side is horizontal distance 1081 ft.

Step2: Solve for vertical distance $x$

Rearrange the tangent formula to isolate $x$:
$x = 1081 \times \tan(32^\circ)$
Calculate $\tan(32^\circ) \approx 0.6249$, then:
$x \approx 1081 \times 0.6249$

Step3: Compute final value

$x \approx 675.5$

Answer:

675.5 feet