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?

Answer 1

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.