How to Find Unknown Lengths in Right Triangles Using the Pythagorean Theorem

Finding unknown lengths in right triangles can be tricky.

But don’t worry! The Pythagorean Theorem can help you.

Here’s a simple guide to follow:

1. Know Your Right Triangle:

   • Make sure you have a right triangle. A right triangle has one angle that is 90 degrees. Sometimes it might be hard to tell, especially in more complicated shapes.

2. Label the Sides:

   • Name the two shorter sides (legs) as $a$ and $b$. The longest side (hypotenuse) should be labeled $c$.
   • Be careful! Labeling sides wrong can cause mistakes in your calculations.

3. Use the Pythagorean Theorem:

   • The theorem tells us that $a^2 + b^2 = c^2$. This might sound easy, but it can get frustrating when you’re trying to find one of the sides.

4. Rearranging the Equation:

   • If you need to find a leg (let's say $a$), change the equation to $a^2 = c^2 - b^2$.
   • This can be confusing if you have more than one unknown side, but it’s important to focus on isolating the variable you want.

5. Calculate and Simplify:

   • Finally, take the square root to find the length. For example: $a = \sqrt{c^2 - b^2}$.
   • Be careful! Make sure to simplify correctly and check your square roots to avoid mistakes.

While these steps can guide you to the right answer, the hardest part is often setting up the problem.

With practice and patience, you will get the hang of these calculations and tackle any challenges that come with the theorem.