Question

A Christmas tree is supported by a wire that is 2 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 23 meters shorter than the height of the tree. What is the height of the tree?

Answer 1

The height of the tree is 35 meters.

Explanation:

Let the height of the tree be x meters, then the length of the wire is

x+2 meters.

The distance from the tree to the anchor is x-23 meters.

So using the pythagoras theorem:

(x + 2)^2 = x^2 +(x -23) ^2

x^2 + 4x + 4 = x^2 + x^2 - 46x + 529

x^2 - 50x + 525 = 0

( x - 15)(x - 35) = 0

x = 15, 35

x cannot be 15 as this would make the distance 15-23 which is negative so x mustr be 35 meters,