Chiu Chang Suann Jing/Examples/Example 8

Example of Problem from

 * There is a bamboo $10$ feet high,
 * the upper end of which being broken down on reaching the ground,
 * the tip is just $3$ feet from the stem;
 * what is the height of the break?

Solution
The height of the break is $4 \tfrac {11} {20}$ feet.

Proof
Let the height of the break be $x$ feet.

The length of the broken section is then $10 - x$ feet.

The broken section forms the hypotenuse of a right triangle.

One of the legs of that right triangle is the remaining stalk of bamboo, which is $x$ feet long.

The other leg is the distance of the end of the tip from the stalk, which is $3$ feet.

Hence: