At a point on the ground 24 ft from the base of a tree the d

At a point on the ground 24 ft from the base of a tree: the distance to the top of the tree is 6 ft more than 2 times the height of the tree. Find the height of the tree. The height of the tree is

Solution

given

base is 24 ft
height is h ft.
the diagonal (hypotenuse) is 2h+ 6
By the Pythagorean Theorem
24² + h² = (2h + 6)² Expand the ()

576 + h² = 4h² + 24h + 36

Gather all terms to one side.
0 = 3h² + 24h – 540 (Divide both sides by 3)
0 = h² + 8h –180 We now need to factor (\"unfoil\") notice that 180 = 18 * 10 and 18 - 10 = 8
0 = (h + 18) (h – 10)
h = – 18 (impossible for height of tree) or h = 10 ft.

the height of tree h = 10ft