Question

You need to remove a tree from your front yard. You have climbed the tree and trimmed off the branches, and you are now ready to chop down the trunk. It is very important that the tree falls in the right direction… away from your house. You have attached a wire to the top of the trunk. You will attach the other end of the wire to the ground and pull it tightly so that when the trunk begins to fall, the wire will pull it in the right direction. The trunk is 24 feet tall and you are going to attach the wire to the ground 10 feet away from the base of the trunk. a) How long must your wire be to reach the ground?

Answer 1

26 feet

Explanation:

Let the length of the required wire =l

The height of the tree =24 cm

We want the tree to fall to the ground 10 feet away from the base.

Ths problem forms a right triangle which I have drawn and attached below.

To determine the length of the wire l required, we use Pythagoras theorem to solve for the hypotenuse of the right triangle.

`B$y Pythagoras theorem: Hypotenuse^2=Opposite^2+Adjacent^2\\$Therefore:\\l^2=24^2+10^2\\l^2=676\\$Take the square root of both sides\\l=√(676)\\ l=26$ feet`

Thw wire must be 26 feet long to reach the ground.