To find the height of the pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit 8 feet tall, measures the angle of elevation to the top of the people to be 36°. To the nearest foot, what is the height of the pole?
First, we need to draw a diagram to understand the problem better.
```
A
|\
| \
8ft| \ height of pole (x)
| \
| \
| \
| \
------------------
120 ft (Base)
```
In this diagram, we can see that the surveyor is standing at point A, 120 feet away from the base of the pole. The transit (or theodolite) is 8 feet tall and measures the angle of elevation to the top of the pole, which is given as 36°.
To find the height of the pole (x), we can use the tangent function:
tan(θ) = opposite / adjacent
In this case, the opposite is the height of the pole (x), and the adjacent is the distance from the surveyor to the base of the pole (120 ft + 8 ft = 128 ft).
So we can write:
tan(36°) = x / 128
To solve for x, we can multiply both sides by 128:
x = 128 * tan(36°)
Using a calculator, we get:
x = 87.6 feet (rounded to the nearest foot)
Therefore, the height of the pole is approximately 88 feet.
To find the height of the pole, we can use trigonometry. In this case, we can use the tangent function.
Let's label the height of the pole as "h". We know that the surveyor moved 120 feet away from the base of the pole. We also know that the transit they were using is 8 feet tall. The angle of elevation to the top of the pole is given as 36°.
Now, let's set up a right triangle with the base being 120 feet, the height being "h", and the angle of elevation being 36°. The opposite side of the triangle is the height of the transit, which is 8 feet.
To find the height of the pole, we need to find the length of the opposite side (h). We can use the tangent function, which is defined as the opposite side divided by the adjacent side.
tan(36°) = opposite/adjacent
tan(36°) = h/120
Now, we can solve for "h" by rearranging the equation:
h = tan(36°) * 120
Calculating this value, we get:
h ≈ 0.7265 * 120
h ≈ 87.18
So, to the nearest foot, the height of the pole is approximately 87 feet.
To find the height of the pole, we can use the tangent function.
Let's label the height of the pole as "h".
We have the following information:
- Distance from the base of the pole to the surveyor: 120 feet
- Height of the transit: 8 feet
- Angle of elevation to the top of the pole: 36°
Using the tangent function, we can set up the following equation:
tan(36°) = h / (120 + 8)
To solve for "h", we can multiply both sides of the equation by (120 + 8):
(120 + 8) * tan(36°) = h
Using a calculator, we can evaluate the right side of the equation:
(120 + 8) * tan(36°) ≈ 123.88
Therefore, to the nearest foot, the height of the pole is approximately 124 feet.