Question

from a hot - air balloon, genesis measures a 40° angle of depression to a landmark thats 799 feet away, measuring horizontally. whats the balloons vertical distance above the ground? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Use the tangent function

The angle of depression is \(40^{\circ}\). The angle of depression is equal to the angle of elevation in the right - triangle formed. Let the vertical distance be \(h\). We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 40^{\circ}\) and the adjacent side \(x = 799\) feet.

Step2: Calculate the vertical distance

We use the formula \(h=x\tan\theta\). Substitute \(x = 799\) and \(\theta=40^{\circ}\). So \(h = 799\times\tan(40^{\circ})\). Since \(\tan(40^{\circ})\approx0.8391\), then \(h=799\times0.8391\).

$$
LATEXBLOCK0
$$

Answer:

\(670.44\) feet