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 tree is 10 feets

Step-by-step explanation:

base is 24 ft

height is h ft.

the diagonal (hypotenuse) is 2h+ 6

By the Pythagorean Theorem

24² + h² = (2h + 6)²

Expand

576 + h² = 4h² + 24h + 36

Gather all terms to one side.

0 = 3h² + 24h – 540 (Divide both sides by 3)

0 = h² + 8h –180

0 = (h + 18) (h – 10)

h + 18 = 0                            h - 10 = 0

h = -18                                   h = 10

h = – 18 (impossible for height of tree) or h = 10 ft.

the height of tree h = 10feets

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