Question

To find the height of a pole, a surveyor moves 160 feet away from the base of the pole and then, with a transit 6 feet tall, measures the angle of elevation to the top of the pole to be 62°. To the nearest foot, what is the height of the pole?

Answer 1

Answer:

306.8 feet

Step-by-step explanation:

Refer the attached figure .

A surveyor moves 160 feet away from the base of the pole i.e. ED = 160 m

Referring the image .

AC=ED=160 m

A transit i.e. AE is 6 feet tall.

AE = CD=6 feet

With a transmit the angle of elevation to the top of the pole to be 62° i.e. ∠BAC = 62°

To Find BC , use tigonometric ratio.

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan 62^{\circ}=\frac{BC}{AC}$

$Tan 62^{\circ}=\frac{BC}{160}$

$1.88*160=BC$

$300.8=BC$

Now, the height of the pole = BC+CD =300.8+6=306.8 feet

Hence the height of the pole is 306.8 feet