A boat is 216 feet from the base of a cliff. If the distance from the top of the cliff to the boat is 17 feet less than twice the height of the cliff to the water, what is the height of the cliff?

We can draw the situation as a right triangle. This yields (216)^2+h^2=(2h-17)^2; 216^2 = 3h^2-68h+17^2 ;

0= 3h^2-68h+17^2-216^2=3h^2-68h-46367. solutions (by quad. form) are 68 +/- sqrt(68^2-4(3)(-46367))/6 . That is, 68 +/- 124.84/6, or 88.806 or 39.194.

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