Question

from a hot - air balloon, isaiah measures a 22° angle of depression to a landmark thats 312 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 \(22^{\circ}\). In the right - triangle formed, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 22^{\circ}\), the opposite side is the vertical distance \(x\) (height of the balloon) and the adjacent side is \(312\) feet. So, \(\tan(22^{\circ})=\frac{x}{312}\).

Step2: Solve for \(x\)

We know that \(x = 312\times\tan(22^{\circ})\). Using a calculator, \(\tan(22^{\circ})\approx0.4040\). Then \(x=312\times0.4040\).

$$x = 312\times0.4040=126.048$$

Answer:

\(126.05\) feet