Question 668529
Let h = height of tree


If "at a point on the ground 24ft from the base of a tree, the distance to the top of the tree if 4ft more than 3 times the height of the tree", then the distance is 3h+4 (and this is the hypotenuse while the other two values are the legs of a right triangle)


Now use the Pythagorean theorem


a^2 + b^2 = c^2


24^2 + h^2 = (3h+4)^2


576 + h^2 = 9h^2 + 24h + 16


0 = 9h^2 + 24h + 16 - h^2 - 576


0 = 8h^2 + 24h - 560

 
8h^2 + 24h - 560 = 0


8(h^2 + 3h - 70) = 0


8(h+10)(h-7) = 0


h+10 = 0 or h-7 = 0


h = -10 or h = 7


Toss out the negative height (since it doesn't make sense) to get the only answer of h = 7


So the height of the tree is 7 ft.