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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 :
[tex]tan\theta = \dfrac{perpendicular}{base}[/tex]
Here, C = 78° , perpendicular = AB = h , base = BC = 3
[tex]tan 78 = \dfrac{h}{3}\\\\h = 4.7 \times 3\\\\h = 14.11[/tex]
Thus, the height of the pole is 322.75 feet.
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