Question

10. A cable is attached to the top of a pole and mounted to the ground 3 feet from the

Answer 1

A cable is attached to the top of a pole and mounted to the ground 3 feet from the base of the pole. The angle of elevation from the mounting to the top of the pole is 78°. The height of the pole is 14.11 feet.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

A cable is attached to the top of a pole and mounted to the ground 3 feet from the base of the pole.

The angle of elevation from the mounting to the top of the pole is 78°.

Let the triangle Δ ABC with AC be the length of the wire and AB be the height of the pole.

Base of the pole = BC = 3 feet

Angle of elevation to the pole = θ = 78°

We have to find the length of the pole that is AB Let the height of the pole be h feet.

According to trigonometry :

$tan\theta = \dfrac{perpendicular}{base}$

Here, C = 78° , perpendicular = AB = h , base = BC = 3

$tan 78 = \dfrac{h}{3}\\\\h = 4.7 \times 3\\\\h = 14.11$

Thus, the height of the pole is 322.75 feet.

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