Math help! Tightrope problem?

Question

The figure illustrates the apparatus for a tightrope walker. Two poles are set y = 50 feet apart, but the point of attachment P for the rope is yet to be determined. 
---> Express the length of the rope L as a function of the distance x from P to the ground. 
---> If the total walk is to be 75 feet, determine the distance from P to the ground.

Answer 1

(a) Redraw the figure .

From the figure sin α = opposite side / hypotenuse 

sin α = (x-2) / L

L = (x-2) / sin α 

So the length of the rope L as a function of the distance x from P to the ground is = (x-2) / sin α 

 

Answer 2

(b) 

Length of the rope is 75 feet

From Pythagoras theory of right angle ,

(hypotenuse)² = (adjacent side)² +  (opposite side)²

75² = 50² + (x-2)²

(x-2)² = 75² - 50² 

(x-2)² = 5625 - 2500

(x-2)² = 3125

x-2 = 55.901

x = 57.901

So the height of the pole is 57.901 feet