Chiu Chang Suann Jing/Examples/Example 7

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Example of Problem from Chiu Chang Suann Jing

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?


The chain is $17$ feet long.


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.


\(\ds \paren {h + 2}^2\) \(=\) \(\ds h^2 + 8^2\) Pythagoras's Theorem
\(\ds \leadsto \ \ \) \(\ds 4 h + 4\) \(=\) \(\ds 64\) simplification
\(\ds \leadsto \ \ \) \(\ds h\) \(=\) \(\ds 15\) simplification

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