Let's break it down step by step.
1. We have a right triangle with a height of 15 and a length of 20.
2. According to the Pythagorean theorem, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
3. Let's call the length of the third side "x".
4. Using the theorem, we can set up the equation: x^2 = 15^2 + 20^2.
5. Now, let's calculate the squares of the known sides: 15^2 = 225 and 20^2 = 400.
6. Substitute these values into the equation: x^2 = 225 + 400.
7. Simplify the equation: x^2 = 625.
8. To find the length of the third side, we need to take the square root of both sides: x = √625.
9. Taking the square root of 625 gives us x = 25.
Therefore, the length of the third side of the triangle is 25.
