Question

NEED HELP ASAP!

to find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit of 8 feet tall, measures the angle of elevation to the top of the pole to be 36°. to the nearest foot, what is the height of the pole?


a. 87 feet
b. 95 feet
c. 71 feet
d. 79 feet

Answer 1

95 feet

Explanation:

Refer the attached figure.

A surveyor moves 120 feet away from the base of the pole i.e. BC = 120 feet.

BC= ED = 120 feet (refer the figure)

Height of transit i.e. DC = 8 feet

DC = EB = 8 feet (refer the figure)

The angle of elevation to the top of the pole to be 36° i.e. ∠ADE = 36°

Height of pole = AE+EB

To find AE use trigonometric ratio

`tan\theta = (Perpendicular)/(Base)`

`tan36^(\circ)= (AE)/(ED)`

`0.726= (AE)/(120)`

`0.726*120= AE`

`87.12 = AE`

Height of pole = AE+EB = 87.12+8 = 95.12 feet≈95 feet

Hence the height of pole is 95 feet

Answer 2

The ratio of height above the transit to the distance to the transit is the tangent of the angle.
.. height = 8 ft +(120 ft)*tan(36°) = 95 ft . . . . . . matches selection B