Question

a person is standing exactly 36 ft from a telephone pole. there is a 30° angle of elevation from the ground to the top of the pole. what is the height of the pole? 12 ft 12√3 ft 18 ft 18√2 ft

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), the adjacent side to the angle of elevation is \(36\) ft (distance from the person to the pole), and the opposite side is the height \(h\) of the pole. So, \(\tan30^{\circ}=\frac{h}{36}\).

Step2: Substitute the value of \(\tan30^{\circ}\)

We know that \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\). Then, \(\frac{1}{\sqrt{3}}=\frac{h}{36}\).

Step3: Solve for \(h\)

Cross - multiply: \(h = \frac{36}{\sqrt{3}}\). Rationalize the denominator: \(h=\frac{36\sqrt{3}}{3}=12\sqrt{3}\) ft.

Answer:

\(12\sqrt{3}\text{ ft}\) (the second option)