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: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=30^\circ$, adjacent side $=36$ ft, opposite side = height of pole ($h$).

Step2: Substitute values into formula

$\tan(30^\circ) = \frac{h}{36}$
We know $\tan(30^\circ) = \frac{1}{\sqrt{3}}$, so:
$\frac{1}{\sqrt{3}} = \frac{h}{36}$

Step3: Solve for $h$

Rearrange to isolate $h$:
$h = \frac{36}{\sqrt{3}}$
Rationalize the denominator:
$h = \frac{36\sqrt{3}}{3} = 12\sqrt{3}$

Answer:

B. $12\sqrt{3}$ ft