Question

to find the height of a pole, a surveyor moves 150 feet away from The base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pool to be 42°. To the nearest foot, what is the height of the pole?

Answer 1

139 feet

EXPLANATION :

The surveyor is 150 feet away from the base of the pole.

The transit is 4 feet tall and the angle of elevation to the top of the pole is 42 degrees.

The illustration will be :

We have a right triangle with an angle of 42 degrees.

The side opposite to the angle is x and the side adjacent to the angle is 150

Using Tangent function :

`\begin{gathered} \tan\theta=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \tan42=(x)/(150) \\ x=150\tan42 \\ x=135.06\sim135\text{ ft} \end{gathered}`

The height of the pole is x + 4

That will be 135 + 4 = 139 ft