Boat is 92 ft. from the base of a cliff. Distance from top of the cliff to the boat is 23 less than twice the height of the cliff. Find height of the cliff.

Question

 I tried using Pythagorean Theorom with one side being 92, one side being X, and the hypotenuse being 2X-23.  I could not figure it out. Any help?

Answer 1

Hi Brittany,

 

You've set up the problem correctly, so you probably made an arithmetic error or forgot to foil the square of the hypotenuse properly.

 

x² + 92² = (2x-23)²

x² + 8464 = 4x² - 92x + 539

0 = 3x² - 92x - 7925

 

The best way to solve this is probably the quadratic formula.

 

x = (92 ± √(92²-4*3*(-7925)) ) / 2*3

x = (92 ± √(103564) ) / 6

x = (92 ± 321.81)/6

Subtracting will give a negative number, so we can ignore that

x = (92 + 321.81)/6

x = 413.81 / 6

x = 68.97 ft