Question

A Christmas tree is supported by a wire that is 9 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 41 meters shorter than the height of the tree. What is the height of the tree

Answer 1

The height of the tree is 80 meters.

Explanation:

Let the height of the Christmas tree be x meters.

Then the length of the wire will be, (x + 9) meters.

And the wire will (x - 41) meters away from the base of the tree.

Consider the diagram below.

Use Pythagoras theorem to solve for x as follows:

`AB^(2)=AC^(2)+CB^(2)`

`(x+9)^(2)=x^(2)+(x-41)^(2)\\\\x^(2)+18x+81=x^(2)+x^(2)-82x+1681\\\\x^(2)-100x+1600=0\\\\x^(2) -80x-20x+1600=0\\\\x(x-80)-20(x-80)=0\\\\(x-80)(x-20)=0`

The value of x is either 80 or 20.

If x = 20, then the base CB will be -21. This is not possible as length is always positive.

Thus, the value of x is 80.

Hence, the height of the tree is 80 meters.