Chiu Chang Suann Jing/Examples/Example 7

Example of Problem from

 * A chain suspended from an upright post has a length of $2$ feet lying on the ground,
 * and on being drawn out to its full length, so as just to touch the ground,
 * the end is found to be $8$ feet from the post.


 * What is the length of the chain?

Solution
The chain is $17$ feet long.

Proof
Let the height of the post be $h$.

The length of the chain is then $h + 2$.

When drawn out to its full length, the chain forms the hypotenuse of a right triangle.

One of the legs of that right triangle is the post, which is $h$ feet long.

The other leg is the distance of the end of the chain from the post, which is $8$ feet.

Hence:

The right triangle in question here is the $\text{8-15-17}$ triangle.