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.)

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.