What is the answer to this problem?

Question

The figure illustrates the apparatus for a tightrope walker. Two poles are set a = 30 feet apart, but the point of attachment P for the rope is yet to be determined. The rope extends diagonally from P and ends at a height 2 ft above ground level, as shown. Express the length L of the rope as a function of the distance x from P to the ground. 

L(x) =  

 

 

Answer 1

Since the length, L, ends 2' above the ground, you will need to draw a triangle with L as the hypotenuse, the base leg stays the same at 30' but the height is (x-2) instead of x.

Then use Pythagorean Theorem and solve. L² = 900 + x² -4x + 4, take the square root of both sides, and you are done. L = √(x ² -4x +904)