Pythagorean Triangle Calculator

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Examples

Take a look at these examples to see how the Pythagorean theorem can be used to find a missing side of a right triangle.

Example 1

💡Find the hypotenuse of a right triangle with legs of 6 and 8.

The Pythagorean theorem is \(a^2 + b^2 = c^2\). Since we know both legs, we can plug 6 and 8 into the formula:

\(6^2 + 8^2 = c^2\)
\(36+64=c^2\)
\(100=c^2\)

Now, take the square root of both sides:

\(\sqrt{100} = c\)
\(10=c\)

Therefore, the hypotenuse is 10!

Example 2

💡Find the missing leg of a right triangle with one leg of 5 and a hypotenuse of 13.

Since we know the hypotenuse, we’ll use 13 for \(c\):

\(a^2+5^2=13^2\)
\(a^2+25=169\)

Now, subtract 25 from both sides:

\(a^2=144\)

Then, take the square root of both sides:

\(a=\sqrt{144}\)
\(a=12\)

Therefore, the missing leg is 12!

Example 3

💡A ladder is leaning against a wall. The ladder is 15 feet long, and the bottom of the ladder is 9 feet away from the wall. How high up the wall does the ladder reach?

In this problem, the ladder is the hypotenuse because it is the longest side of the right triangle. The distance from the wall is one leg, and the height up the wall is the missing leg.

\(a^2+9^2=15^2\)
\(a^2+81=225\)

Now, subtract 81 from both sides:

\(a^2=144\)

Then, take the square root of both sides:

\(a=\sqrt{144}\)
\(a=12\)

Therefore, the ladder reaches 12 feet up the wall!

More Resources

Click below to watch a comprehensive video about the Pythagorean theorem, along with other helpful resources to help you fully grasp the topic!

Learn More About The Pythagorean Theorem Here!