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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.

Respuesta :

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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:

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

[tex]tan 44=\frac{opposite}{adjacent}[/tex]

[tex]tan44=\frac{x}{140}[/tex]

[tex]x=140tan44=135.20[/tex]

So the total length of pole is = [tex]135.2+4=139.2[/tex]

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

Hope it will help :)

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