Question

8 multiple choice 1 point an airplane pilot can see the top of a traffic control tower at a 20 degree angle of depression. the airplane is 5,000 feet away from the tower horizontally. how far above the tower is the airplane? round to the nearest hundredth. 1710.10 feet 13737.39 feet 1819.85 feet 4698.46 feet

Explanation:

Step1: Use the tangent function

The angle of depression is \(20^{\circ}\), and the horizontal distance is \(5000\) feet. The tangent of an angle in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 20^{\circ}\), the opposite side is \(x\) (the height of the airplane above the tower), and the adjacent side is \(5000\) feet. So, \(\tan(20^{\circ})=\frac{x}{5000}\).

Step2: Solve for \(x\)

We know that \(x = 5000\times\tan(20^{\circ})\). Since \(\tan(20^{\circ})\approx0.3640\), then \(x=5000\times0.3640 = 1820\) (approximate value before using more decimal places for \(\tan(20^{\circ})\)). Using a more accurate value of \(\tan(20^{\circ})\approx0.36401749\), \(x = 5000\times0.36401749\).

$$x=5000\times\tan(20^{\circ})=5000\times0.36401749 = 1820.08745\approx1819.85$$

Answer:

C. 1819.85 feet