Question

from a hot-air balloon, nayeli measures a 38° angle of depression to a landmark thats 908 feet away, measuring horizontally. whats the balloons vertical distance above the ground? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use the tangent function

Let \(h\) be the vertical distance. The angle of depression is \(38^{\circ}\), and the horizontal distance is \(908\) feet. The angle of depression is equal to the angle of elevation from the landmark to the balloon. So, \(\tan\theta=\frac{h}{d}\), where \(\theta = 38^{\circ}\) and \(d = 908\) feet.

Step2: Solve for \(h\)

We know that \(h=d\times\tan\theta\). Substitute \(d = 908\) and \(\theta=38^{\circ}\) into the formula. \(h = 908\times\tan(38^{\circ})\). Since \(\tan(38^{\circ})\approx0.7813\), then \(h=908\times0.7813 = 709.4204\)

Answer:

\(709.4\) feet