The Pythagorean Theorem is a great tool when you’re working with right triangles!

So, what does it say?

In a right triangle, the square of the length of the longest side (called the hypotenuse) is equal to the sum of the squares of the other two sides (called the legs).

We can write it like this:

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

Here, $c$ is the hypotenuse, and $a$ and $b$ are the legs.

How to Find a Missing Leg:

1. Identify the Hypotenuse and Legs:

   • First, look for the right angle. It usually has a small square in the corner. The side across from this angle is your hypotenuse. The other two sides are the legs.

2. Assign Values:

   • If you know one leg and the hypotenuse, you can put those values into the equation. For example, if you know $c$ (the hypotenuse) and $a$ (one leg), then you are trying to find $b$ (the other leg).

3. Rearranging the Equation:

   • To solve for a leg, you can change the equation a bit. Let’s say you want to find $b$:

   $b^2 = c^2 - a^2$

4. Plugging in Values:

   • Now put the known values in. If $c = 10$ and $a = 6$, it looks like this:

   $b^2 = 10^2 - 6^2$
   $b^2 = 100 - 36$
   $b^2 = 64$

5. Solving for $b$:

   • Finally, take the square root of both sides:

   $b = 8$

And that’s it! You’ve found the missing leg.

This method is really useful for many kinds of problems, whether you’re doing school projects or working on real-life tasks like building or finding directions.