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 \(x = 36\) ft (distance from the person to the pole), and the opposite side \(y\) (height of the pole) is what we want to find. So, \(\tan30^{\circ}=\frac{y}{36}\).

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

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

Step3: Solve for \(y\)

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

Answer:

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