a person is standing exactly 36 ft from a telephone pole. there is a 30° angle of elevation from the ground…

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

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

Answer

Explanation:

Step1: Recall tangent - function formula

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

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

We know that $\tan30^{\circ}=\frac{\sqrt{3}}{3}$. Then $\frac{\sqrt{3}}{3}=\frac{h}{36}$.

Step3: Solve for $h$

Cross - multiply: $h = 36\times\frac{\sqrt{3}}{3}=12\sqrt{3}$ ft.

Answer:

B. $12\sqrt{3}$ ft