Question

question
from a hot - air balloon, juan measures a ( 36 ^ { circ } ) angle of depression to a landmark thats
602 feet away, measuring horizontally. whats the balloons vertical distance above the
ground? round your answer to the nearest tenth of a foot if necessary.
answer
attempt 1 out of 2
feet
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Explanation:

Step1: Use the tangent function

The angle of depression is \(36^{\circ}\). The horizontal distance \(x = 602\) feet. Let the vertical distance be \(h\). Since the angle of depression is equal to the angle of elevation in this right - triangle situation (alternate interior angles), \(\tan\theta=\frac{h}{x}\), where \(\theta = 36^{\circ}\) and \(x = 602\) feet.

Step2: Solve for \(h\)

We know that \(h=x\tan\theta\). Substitute \(x = 602\) and \(\theta = 36^{\circ}\). Using a calculator, \(\tan(36^{\circ})\approx0.7265\). Then \(h = 602\times0.7265\).

$$h=602\times0.7265=437.353$$

Answer:

\(437.4\) feet