Pythagorean Theorem Calculator

What is the Pythagorean Theorem?

The Pythagorean Theorem is like a magic rule for right triangles! It tells us how the sides of a right triangle are related. Imagine you have a triangle with a right angle (like the corner of a square). The Pythagorean Theorem helps us find the length of any side if we know the other two!

How to Calculate Using the Pythagorean Theorem

To use the Pythagorean Theorem, we add the squares of the two shorter sides and set it equal to the square of the longest side. It's like fitting squares onto each side of the triangle and seeing how they compare!

Formula

We write the Pythagorean Theorem like this:

\[ a^2 + b^2 = c^2 \]

This means:

• \(a\) and \(b\) are the lengths of the two shorter sides (called the legs)
• \(c\) is the length of the longest side (called the hypotenuse)
• The little 2 means we're squaring the numbers (multiplying them by themselves)

Calculation Steps

1. Identify the right triangle and its sides
2. Square the length of each leg (a and b)
3. Add these squared values together
4. To find c, take the square root of the sum
5. If you know c and one leg, subtract the square of the known leg from c² and take the square root

Example and Visual Representation

Let's use a real-world example:

Imagine a ladder leaning against a wall. The bottom of the ladder is 3 feet from the wall, and the top of the ladder reaches 4 feet up the wall. How long is the ladder?

We can use the Pythagorean Theorem to find out!

• a = 3 feet (distance from wall to ladder base)
• b = 4 feet (height up the wall)
• c = length of the ladder (what we want to find)

Let's solve it:

\[ 3^2 + 4^2 = c^2 \]

\[ 9 + 16 = c^2 \]

\[ 25 = c^2 \]

\[ c = \sqrt{25} = 5 \]

The ladder is 5 feet long!

In this picture, we can see how the ladder forms a right triangle with the wall and floor. The Pythagorean Theorem helped us find the length of the ladder!