SOLUTION: At a point on the ground 80ft from the base of a tree, the distance to the top of the tree is 11ft more than 2 times the height of the tree. Find the height of the tree. (Simplify

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Question 269651: At a point on the ground 80ft from the base of a tree, the distance to the top of the tree is 11ft more than 2 times the height of the tree. Find the height of the tree. (Simplify your answer. Round to the nearest foot as needed.)

Answer by mananth(16946) About Me  (Show Source):
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At a point on the ground 80ft from the base of a tree, the distance to the top of the tree is 11ft more than 2 times the height of the tree. Find the height of the tree. (Simplify your answer. Round to the nearest foot as needed.)
let the height of the tree be x
horizontal distance from the tree is 80 feet
distance to the top of the tree is 2x+11
using the pythagoras theorem we get
(x+2)^2= x^2 + 80^2
x^2+4x+4=x^2 +80^2
x^2-x^2 +4x=80^2
4x=80^2
x=80^2 /4
x= 80^20
x=1600
the height of the tree is 1600 feet.