Question

To find the height of a 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 pole to be 26. to the nearest foot, what is the height of the pole

Answer 1

Refer to the figure.
Let AB be the height of the pole; CD be the height of the transit; BC is the distance from the base of the pole to the transit.

Triangle ADE is a right triangle with angle D measuring 26 degrees. Using the tangent function, we have

`tan\:26^(\circ) =(AE)/(120)`
So,

`AE=120\:tan\:26^(\circ)`

`AE=58.53\:`

Therefore, the overall height of the pole is

`AB=58.53+8=66.53\:feet`

The height of the pole is 66.53 feet.