Question

from a hot-air balloon, adriel measures a $22^\circ$ angle of depression to a landmark thats 743 feet away, measuring horizontally. whats the balloons vertical distance above the ground? round your answer to the nearest hundredth of a foot if necessary.
answer attempt 1 out of 3

Explanation:

Step1: Define variables and trigonometric ratio

Let $h$ = vertical height of the balloon. The angle of depression equals the angle of elevation from the landmark to the balloon, so we use $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=22^\circ$, adjacent side = 743 ft, opposite side = $h$.

Step2: Substitute values and solve for $h$

$$\tan(22^\circ) = \frac{h}{743}$$
Rearrange to solve for $h$:
$$h = 743 \times \tan(22^\circ)$$
Calculate $\tan(22^\circ) \approx 0.4040$, so:
$$h \approx 743 \times 0.4040$$

Step3: Compute the final value

$$h \approx 299.17$$

Answer:

299.17 feet