Question

To find the height of a pole, a surveyor uses a theodolite. The theodolite is 4 ft tall. The surveyor stands 140 feet away from the base of the pole. Then she measures the angle of elevation to the top of the pole to be 44°. What is the height of the pole? Round the answer to the nearest foot.

Answer 1

tan 44° = x/140

x = 140 tan 44°

x approx = 140 * 0.9657 = 135.198

Remember, we need to add another 4 feet, so the answer would be 139.198 feet

Answer 2

Explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The height of pole will be in two parts, upper part is x and second will be the height of theodolite which is already given as 4 feet.

Using SOH CAH TOA in triangle ABC

`tan 44=(opposite)/(adjacent)`

`tan44=(x)/(140)`

`x=140tan44=135.20`

So the total length of pole is =
`135.2+4=139.2`

Rounding to the nearest feet, the height of pole is 139 feet. : Answer

Hope it will help :)