Question

from a hot - air balloon, enola measures a 22° angle of depression to a landmark thats 310 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 \(22^{\circ}\). The horizontal distance (adjacent side) is \(310\) feet. Let the vertical distance (opposite side) be \(h\). The tangent of an angle in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Since the angle of depression is equal to the angle of elevation from the landmark to the balloon, \(\theta = 22^{\circ}\), \(adjacent = 310\) and \(opposite=h\). So, \(\tan(22^{\circ})=\frac{h}{310}\).

Step2: Solve for \(h\)

We can rewrite the equation as \(h = 310\times\tan(22^{\circ})\). We know that \(\tan(22^{\circ})\approx0.4040\). Then \(h=310\times0.4040 = 125.24\)

Answer:

\(125.24\) feet