A vertical pole 32 feet tall stands on a hillside that makes an angle of 17° with the horizontal line. Determine the approximate length of cable that would be needed to reach
from the top of the pole to a point 56 feet downhill from the base of the pole. Round answer to two decimal places.
A. 72.17 feet
D. 68.24 feet
B. 76.77 feet
E. 55.79 feet
C. 63.98 feet
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dooof dooof · Answer 1 · 2021-06-11T16:06:46+02:00

Answer:

The 72 feet is measured on the slope, not out from the pole horizontally. I get

top of pole is at

40 + 72 sin17°

downhill point is

72 cos 17°

from point beneath the pole

cable^2 = (40+72 sin17°)^2 + (72 cos 17°)^2

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kapoorprachi783 kapoorprachi783 · Answer 2 · 2022-05-26T10:15:52+02:00

The correct answer is option b) 76.77

The 56 feet is measured on the slope, not out from the pole horizontally.

The top of the pole is at

32 + 56 sin17°

Downhill point is

56 cos17°

From a point beneath the pole

⇒ cable^2 = (32 + 56 sin17°)^2 + (56 cos17°)^2

⇒ cable^2 = 96.74 + 53.553

⇒ cable^2 = 150.29

Dividing both sides by 2

⇒ cable = 75.15 (76 approx)

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