To find the missing side lengths of a right triangle, we can use something called the Pythagorean Theorem. This rule helps us understand how the sides of a right triangle relate to each other.

Here’s the basic idea:

The theorem tells us that if we take the two shorter sides (we call these legs) and square their lengths, the total will equal the square of the longest side (this side is called the hypotenuse). We can write this rule like this:

$a^2 + b^2 = c^2$

In this equation:

• $a$ and $b$ are the lengths of the legs.
• $c$ is the length of the hypotenuse.

Steps to Find Missing Side Lengths:

1. Identify the Sides: First, figure out which side lengths you know and which one you need to find.

2. Plug in Known Values:

   • If you know the lengths of both legs ($a$ and $b$), you can find the hypotenuse ($c$) like this: $c = \sqrt{a^2 + b^2}$
   • If you know one leg and the hypotenuse ($c$), you can find the missing leg ($a$) by rearranging the formula: $a = \sqrt{c^2 - b^2}$

3. Calculate: Use a calculator to do the math.

This method is really helpful! I remember using it in school for different triangle problems. It made understanding triangles much easier for me. Once you get the hang of it, you’ll feel more confident facing many geometry tasks!