Pythagorean Theorem Worksheets - Free Printable

Looking at the worksheet, I need to find the missing side of each right triangle using the Pythagorean Theorem: a² + b² = c², where c is always the hypotenuse (the longest side, opposite the right angle).

Let me check each problem one by one:

Top Left Triangle:
- Given: b = 40, c = 50, find a
- Formula: a² + 40² = 50²
- Calculate: a² + 1600 = 2500
- Subtract: a² = 900
- Square root: a = √900 = 30 ✓ Correct

Top Right Triangle:
- Given: a = 42, c = 70, find b
- Formula: 42² + b² = 70²
- Calculate: 1764 + b² = 4900
- Subtract: b² = 3136
- Square root: b = √3136 = 56 ✓ Correct

Middle Left Triangle:
- Given: a = 36, c = 60, find b
- Formula: 36² + b² = 60²
- Calculate: 1296 + b² = 3600
- Subtract: b² = 2304
- Square root: b = √2304 = 48 ✓ Correct

Middle Right Triangle:
- Given: a = 36, b = 27, find c
- Formula: 36² + 27² = c²
- Calculate: 1296 + 729 = 2025
- Square root: c = √2025 = 45 ✓ Correct

Bottom Left Triangle:
- Given: a = 9, b = 40, find c
- Formula: 9² + 40² = c²
- Calculate: 81 + 1600 = 1681
- Square root: c = √1681 = 41 ✓ Correct

Bottom Right Triangle:
- Given: b = 105, c = 119, find a
- Formula: a² + 105² = 119²
- Calculate: a² + 11025 = 14161
- Subtract: a² = 3136
- Square root: a = √3136 = 56 ✓ Correct

All answers shown in the answer key are correct!

Final Answer:
The solutions provided in the answer key are all correct. Each triangle's missing side was found properly using the Pythagorean Theorem (a² + b² = c²), and all calculations check out.