In this page we practice using the Pythagorean Theorem to solve different right triangle examples step by step.
We also practice:
- finding the hypotenuse
- finding a missing side
- using square roots
- writing exact answers and decimal approximations
Example 1 – Find the Hypotenuse
Find the hypotenuse \(c\) when \(a=6\) and \(b=8\).
Step 1: Substitute \(a=6\) and \(b=8\)
\(6^2 + 8^2 = c^2\)
Step 2: Simplify
\(36 + 64 = c^2\)
Step 3: Add
\(100 = c^2\)
Step 4: Take square root both sides and since length is always positive, we get
\(c = 10\)
Example 2 – Find the Hypotenuse
Find \(c\) when \(a=5\) and \(b=12\).
Step 1:
\(5^2 + 12^2 = c^2\)
Step 2:
\(25 + 144 = c^2\)
Step 3:
\(169 = c^2\)
Step 4:
\(c = 13\)
Example 3 – Find a Missing Side
Find the side \(a\) when \(c=10\) and \(b=6\).
Step 1: Substitute \(c=10\) and \(b=6\)
\(a^2 + 6^2 = 10^2\)
Step 2: Simplify
\(a^2 + 36 = 100\)
Step 3: Subtract \(36\) from both sides
\(a^2 = 64\)
Step 4: Take square root
\(a = 8\)
Example 4 – Find Another Side
Find the side \(b\) when \(c=13\) and \(a=5\).
Step 1:
\(5^2 + b^2 = 13^2\)
Step 2:
\(25 + b^2 = 169\)
Step 3:
\(b^2 = 144\)
Step 4:
\(b = 12\)
Example 5 – Decimal Answer
Find the hypotenuse \(c\) when \(a=2\) and \(b=3\).
Step 1:
\(2^2 + 3^2 = c^2\)
Step 2:
\(4 + 9 = c^2\)
Step 3:
\(13 = c^2\)
Step 4:
\(c = \sqrt{13} \approx 3.61\)
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)