Answer :
To find the height of the telephone pole given the distance from the pole and the angle of elevation, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is defined as the ratio of the opposite side (height of the pole) to the adjacent side (distance from the pole).
Given:
- Distance from the pole (adjacent side) = 36 ft
- Angle of elevation = 30°
We need to find the height of the pole (opposite side).
The tangent of the angle is given by:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Substituting the given values:
[tex]\[ \tan(30^\circ) = \frac{\text{height of the pole}}{36 \text{ ft}} \][/tex]
We know from trigonometry that:
[tex]\[ \tan(30^\circ) = \frac{\sqrt{3}}{3} \][/tex]
Thus,
[tex]\[ \frac{\sqrt{3}}{3} = \frac{\text{height of the pole}}{36 \text{ ft}} \][/tex]
To find the height of the pole, we solve for the opposite side:
[tex]\[ \text{height of the pole} = 36 \text{ ft} \times \frac{\sqrt{3}}{3} \][/tex]
Simplifying this:
[tex]\[ \text{height of the pole} = 36 \times \frac{\sqrt{3}}{3} = 12 \sqrt{3} \text{ ft} \][/tex]
So, the height of the pole is:
[tex]\[ 12 \sqrt{3} \text{ ft} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{12 \sqrt{3} \text{ ft}} \][/tex]
Given:
- Distance from the pole (adjacent side) = 36 ft
- Angle of elevation = 30°
We need to find the height of the pole (opposite side).
The tangent of the angle is given by:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
Substituting the given values:
[tex]\[ \tan(30^\circ) = \frac{\text{height of the pole}}{36 \text{ ft}} \][/tex]
We know from trigonometry that:
[tex]\[ \tan(30^\circ) = \frac{\sqrt{3}}{3} \][/tex]
Thus,
[tex]\[ \frac{\sqrt{3}}{3} = \frac{\text{height of the pole}}{36 \text{ ft}} \][/tex]
To find the height of the pole, we solve for the opposite side:
[tex]\[ \text{height of the pole} = 36 \text{ ft} \times \frac{\sqrt{3}}{3} \][/tex]
Simplifying this:
[tex]\[ \text{height of the pole} = 36 \times \frac{\sqrt{3}}{3} = 12 \sqrt{3} \text{ ft} \][/tex]
So, the height of the pole is:
[tex]\[ 12 \sqrt{3} \text{ ft} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{12 \sqrt{3} \text{ ft}} \][/tex]
