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

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

Answer Link

wifilethbridge wifilethbridge · Answer 2 · 2019-02-22T05:12:50+01:00

Answer:

95 feet

Step-by-step 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

[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]

[tex]tan36^{\circ}= \frac{AE}{ED}[/tex]

[tex]0.726= \frac{AE}{120}[/tex]

[tex]0.726*120= AE[/tex]

[tex]87.12 = AE[/tex]

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

Hence the height of pole is 95 feet