🔢 Math Calculator

📐 How It Works

Applies a² + b² = c² to find any side of a right triangle given the other two. Named for Pythagoras but known to Babylonians ~4,000 years ago.

🔢 Worked Examples

• 3-4-5: √(9+16) = 5
• 5-12-13: √(25+144) = 13
• a=7, b=24: c=25
• Diagonal of 1×1 square = √2 ≈ 1.414

📋 Common Use Cases

• Construction and carpentry — squaring a room
• Navigation — straight-line distance between two points
• Screen diagonal calculation (width² + height²)
• GPS path calculations

💡 Did You Know?

The 3-4-5 right triangle has been used by Egyptian builders for over 4,000 years to create perfect right angles — by tying knots at equal intervals in a rope, forming a 12-unit loop (3+4+5=12), then stretching it into a triangle.

⚠️ Common Mistake

Using the theorem on non-right triangles — it only works for the hypotenuse (longest side, opposite the 90° angle). For other triangles, use the law of cosines.