Answer to Question #175955 in Trigonometry for Ekene Duru

Question

The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 70

 feet tall. To keep it upright, a support cable needs to be attached to the top of the pole so that the cable forms a 60∘

 angle with the ground.

1. How long is the cable?
2. How far from the pole should the cable be attached to the ground?

Answer 1

A right angle triangle will be formed when the support cable is tied to the top of the center pole.

Using the knowledge of trigonometry (SOH CAH TOA)

1) sin thetha = opposite/hypotenuse

Where opposite = length of center pole

hypotenuse = length of support cable

And thetha = 60°

sin 60° = 70 / length of support cable

Length of support cable = 70/0.866

Length of support cable = 80.83 feet

2) tan thetha = opposite/adjacent

where adjacent = distance of center pole from support cable on the ground

cos 60° = 70/ distance of center pole from support cable on the ground

Distance of center pole from support cable on the ground = 70/0.5 = 35 feet.