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)?

A)53.53 feet

B)74.62 feet C)126.11 feet D) 322.75 feet

Answer 1

You can solve this problem and calculate the height of the pole, by following the steps below:

Tan(α)=Opposite leg/Adjacent leg

α is the angle of elevation (α=67°).
The opposite leg is the height of the pole. Let's call it "x".
Adjacent leg=137 feet

When you substitute these values into the formula Tan(α)=Opposite leg/Adjacent leg, you have:

Tan(α)=Opposite leg/Adjacent leg
Tan(67°)=x/137

You must clear the "x"

x=137xTan(67°)
x=322.75

What is the height of the pole?

The answer is: The height of the pole is 322.75 feet.