SOLUTION: Lightning hit a tree three-eights of the distance up the trunk from the ground and broke the tree so that its top landed 40 ft from the base of the trunk. Creates a triangle. Quest

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Question 7323: Lightning hit a tree three-eights of the distance up the trunk from the ground and broke the tree so that its top landed 40 ft from the base of the trunk. Creates a triangle. Question is How tall was the tree originally. I said a2+b2=c2, so 1600+.140625(change 3/8 to decimal)= then it all falls apart from there.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let h ft. be the original height of tree.
The remaining upright piece ater the lightning strike is (3/8)h ft.
The broken-off piece is then (5/8)h ft. This forms the hypotenuse of the right triangle, whose base is 40 ft.
Using the Pythagorean theorem, c%5E2+=+a%5E2+%2B+b%5E2 we can write:
%28%285%2F8%29h%29%5E2+=+%28%283%2F8%29h%29%5E2+%2B+%2840%29%5E2 Subtract %283%2F8%29h%5E2 from both sides.
%281%2F4%29h%5E2+=+40%5E2 Multiply both sides by (4/1).
h%5E2+=+40%5E2%284%29 Take the square root of both sides.
h+=+40%282%29
h+=+80+ft.