Question

A vertical pole 40 feet tall stands on a hillside that makes an angle of 17o with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 72 feet downhill from the base of the pole. Round answer to four decimal places.

Answer 1

Answer: The approximate length of cable that would be needed to reach from the top of the pole to a point 72 feet downhill from the base of the pole is 110.8706 feet.

Explanation:

It is given that the height of pole is 40 feet and the angle with the horizontal is 17 degree. The point is 72 feet downhill from the base of the pole.

Draw the diagram as shown below.

The angle BAC and the given angle are supplementary angles. So,

$\angle BAC=180^{\circ}-17^{\circ}$

$\angle BAC=163^{\circ}$

From the figure the sides are b = 40 feet and c = 72 feet. The $\angle A=163^{\circ}$.

According to Cosine Rule

$a^2=b^2+c^2-2ab\cos A$

$a^2=(40)^2+(72)^2-2(40)(72)\cos (163^{\circ})$

$a^2=1600+5184-5760(-0.9563)$

$a^2=6784+5508.288$

$a^2=12292.288$

$a\approx 110.8706$

Therefore, the length of cable is approximately 110.8706 feet.