Question

A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?

Answer 1

Answer:

The height of the pole is 322.75 feet.

Step-by-step explanation:

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

Length between the point of attachment of wire from base of the pole = BC = 137 feet

Angle of elevation to the pole = θ = 67°

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

According to trigonometry :

$\tan C=\frac{\text{perpendicular}}{\text{base}}$

Here, C = 67° , perpendicular = AB = h , base = BC = 137

Substitute the values,

$\tan 67^{\circ}=\frac{AB}{BC}$

$\tan 67^{\circ}=\frac{h}{137}$

$h=\tan 67^{\circ} \times 137$

$h=322.75$

Thus, the height of the pole is 322.75 feet.