Even though it was now middle of winter, Jack hauled out his ladder and placed his ladder against the side of the house and began to climb. He had some bad luck when he reached the half-way point. The ground was a frozen sheet of ice and the base of his ladder slipped out and the top slid down the side of the house. Jack, clinging to the center rung, wound up moving from Point A on the side of his house to Point B on the ground.

Describe the path Jack traveled.

It's actually part of a circle. The reason why is if you take the height on the wall, length the bottom is away from the bottom of the wall, and the ladder as a triangle and connect the midpoint of the ladder to where wall meets ground, you will find this midpoint connection is always equal.

Start by taking the two triangles made by Jack's location, the ladder-meets the ground, and the midpoint of the ground and the midpoint of the ground, ground-meets the wal and Jack's location. Since the midpoint of the ladder hypoteneuse is over the midpoint of the ground leg, those two bottom sides are equal, and obviously the height up to Jack and the angle are equal. So this means SAS and the hypotenueses of the smaller triangles are equal as well:

Posted by Gamer on 2004-07-27 11:18:23