On this page, we practice using the Pythagorean formula to find missing sides in right triangles.
We practice:
- finding the hypotenuse
- finding a missing side
- working with larger numbers
- simplifying square roots
Remember
The Pythagorean formula is:
\(c^2=a^2+b^2\)
Where:
- \(c\) is the hypotenuse.
- The hypotenuse is the longest side.
- The hypotenuse is opposite the \(90^\circ\) angle.
- \(a\) and \(b\) are the other two sides of the right triangle.
To find the hypotenuse, add the squares of the two known sides.
To find another missing side, subtract the square of the known side from the square of the hypotenuse.
Example 1 – Find the Hypotenuse
Find the hypotenuse \(x\) of the right triangle.
The two known sides are \(3\) and \(4\).
Solution:
\(x^2=3^2+4^2\)
\(x^2=9+16\)
\(x^2=25\)
Take the square root of both sides:
\(x=\sqrt{25}\)
\(x=5\)
So, the hypotenuse is \(5\).
Example 2 – Find a Missing Side
Find the missing side \(x\) of the right triangle.
Hypotenuse \(=5\)
Known side \(=4\)
Solution:
\(5^2=x^2+4^2\)
\(25=x^2+16\)
Subtract \(16\) from both sides:
\(x^2=9\)
Take the square root of both sides:
\(x=\sqrt{9}\)
\(x=3\)
So, the missing side is \(3\).
Example 3 – Find a Missing Side
Find the missing side \(x\) of the right triangle.
Hypotenuse \(=13\)
Known side \(=5\)
Solution:
\(13^2=x^2+5^2\)
\(169=x^2+25\)
Subtract \(25\) from both sides:
\(x^2=144\)
Take the square root of both sides:
\(x=\sqrt{144}\)
\(x=12\)
So, the missing side is \(12\).
Example 4 – Find the Hypotenuse
Find the hypotenuse \(x\) of the right triangle.
The two known sides are \(8\) and \(15\).
Solution:
\(x^2=8^2+15^2\)
\(x^2=64+225\)
\(x^2=289\)
Take the square root of both sides:
\(x=\sqrt{289}\)
\(x=17\)
So, the hypotenuse is \(17\).
Example 5 – Find the Hypotenuse
Find the hypotenuse \(y\) of the right triangle.
The two known sides are \(1\) and \(1\).
Solution:
\(y^2=1^2+1^2\)
\(y^2=1+1\)
\(y^2=2\)
Take the square root of both sides:
\(y=\sqrt{2}\)
As a decimal:
\(y \approx 1.41\)
So, the hypotenuse is:
\(\sqrt{2} \approx 1.41\)
Practice
- More Examples (Current page)
Continue Learning
- Pythagorean Formula
- Pythagoras Theorem (a² + b² = c²) – Visual Proof 1
- Pythagoras Theorem (a² + b² = c²) – Visual Proof 2
- Pythagoras Theorem (Example)