Question

the angle of depression from a bird sitting on top of a telephone pole to the base of a tree is 63°. if the telephone pole is 18 feet tall, what is the distance between the pole and the tree? round to the nearest tenth. (see yellow hint below.) 16.0 ft 35.3 ft 20.2 ft 9.2 ft

Explanation:

Step1: Use the tangent function

The angle of depression is equal to the angle of elevation. Let the distance between the pole and the tree be \(x\). We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 63^{\circ}\), the opposite side is \(18\) ft (height of the pole). So, \(\tan63^{\circ}=\frac{18}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{18}{\tan63^{\circ}}\). Using a calculator, \(\tan63^{\circ}\approx1.9626\). Then \(x = \frac{18}{1.9626}\approx9.2\).

Answer:

\(9.2\) ft