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 feetB)74.62 feetC)126.11 feetD)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.