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
6² + 8² = c²

Step 2: Simplify
36 + 64 = c²

Step 3: Add
100 = c²

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:
5² + 12² = c²

Step 2:
25 + 144 = c²

Step 3:
169 = c²

Step 4:
c = 13

Example 3 – Find a Missing Side

Find the side aaa when c=10 and b=6.

Step 1: Substitute c=10 and b=6
a² + 6² = 10²

Step 2: Simplify
a² + 36 = 100

Step 3: Subtract 36 from both sides
a² = 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:
5² + b² = 13²

Step 2:
25 + b² = 169

Step 3:
b² = 144

Step 4:
b = 12

Example 5 – Decimal Answer

Find the hypotenuse c when a=2 and b=3.

Step 1:
2² + 3² = c²

Step 2:
4 + 9 = c²

Step 3:
13 = c²

Step 4:
c = √13 ≈ 3.61

Practice

• More Examples

• Take the Quiz

Continue Learning

1. Pythagorean Formula
2. Pythagoras Theorem (a² + b² = c²) – Visual Proof 1
3. Pythagoras Theorem (a² + b² = c²) – Visual Proof 2
4. Pythagoras Theorem (Example)

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