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

Question

2 years ago

10

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.

Mathematics

2 answers:

Ad libitum [116K] · Answer 1 · 2022-07-10T13:59:15+03:00

Ad libitum [116K]2 years ago

6 0

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

makvit [3.9K] · Answer 2 · 2022-07-10T15:50:10+03:00

Answer:

Step-by-step 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

$tan 44=\frac{opposite}{adjacent}$

$tan44=\frac{x}{140}$

$x=140tan44=135.20$

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 :)