Assumption: let the water depth be x.
Using Pythagorean Theorem:
5? +x？ =(x+ 1)？
25+x？ =(x+ 1)？
x= 12
x+ 1= 13
Answer: Water depth 12 feet, reed 13 feet.
The analysis is shown in Figure 4:
Extended data:
In the process of solving this problem, Pythagorean theorem is used, which is defined as follows:
In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse. If the sum of the lengths of the two right sides of a right triangle and the length of the hypotenuse are, it can be expressed in mathematical language: Pythagorean theorem is a special case of cosine theorem.
Pythagorean theorem is a basic geometric theorem, which means that the sum of the squares of two right angles of a right triangle is equal to the square of the hypotenuse. In ancient China, right-angled triangles were called Pythagorean Theorem, the smaller right-angled side was a hook, the other longer right-angled side was a chord, and the hypotenuse was a chord, so this theorem was called Pythagorean Theorem, and some people called it quotient height theorem.