Question

At a point on the ground 70 ft from the base of the tree, the distance to the top of the tree is 2 ft more than 3 times in the highest of the tree find the highest of the tree

Answer 1

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Answer:

24 ft

Explanation:

Let x represent the height of the tree. The geometry can be represented by a right triangle with a base of 70 ft, a height of x ft, and a hypotenuse of 2+3x ft. The Pythagorean theorem tells us the relationship ...

x^2 +70^2 = (2+3x)^2

8x^2 +12x -4896 = 0 . . . .put in standard form

2x^2 +3x -1224 = 0 . . . . remove a common factor of 4

(2x +51)(x -24) = 0 . . . . . factor

The only positive solution is x = 24.

The height of the tree is 24 feet.