Parachute word problem

Question

If I had a round parachute that was 26ft in diameter and it was lifted at the center pole 17ft high. How long would the ropes from the ends perimeter of the parachute be staked in the ground away from the parachute to have a height of 9 ft at the outside of the parachute?

Answer 1

The parachute lifted by the center pole would make an inverted

cone shaped figure

 

The center pole, distance from center pole on the ground to the 

stakes, and distance running from the ground diagonally

up along the parachute to the peak make a right triangle

 

Let X be the length of rope needed to go from edge of parachute to 

the stakes in ground

 

13 is radius of parachute and is length of parachute hanging

diagonally down from center pole

 

Drawing this figure you will see two triangles which are similar, so we 

can set the proportion:

 

            X / 9 ft.  =  (X + 13 ft.) / 17

 

                  cross multiply

 

                 17X  =  9X + 117

 

                  8X   =  117

 

                     X  =  14.6 ft.

 

Ropes must be 14.6 ft. long