# Precalculus

An 18 m tall tree is broken during a severe storm. The distance from the base of the trunk to the point where the tip touches the ground is 12 m. At what height did the tree break?

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1. the standard 5-12-13 triangle fits the bill, but algebraically,

If the tree broke at height x,

12^2 + x^2 = (18-x)^2
x = 5

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2. x^2 + 12^2 = (18-x)^2
x^2 + 144 + x^2 - 36x + 324
144 = -36x + 324
-180 = -36x
-180/-36 = -36x/-36
5 = x

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3. Mehtab made a slight error in his second step,it was suppose to be = instead or +

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