PanMaths.comFree Printable Math Formula Reference Sheet
Pythagorean Theorem
Geometry • Grades 7, 8, 9, 10
Geometry
Pythagorean Theorem
The fundamental relationship in right triangles.
The Formula
a² + b² = c²
Used for: Finding the unknown side length in any right-angled triangle
aLength of adjacent leg
bLength of opposite leg
cHypotenuse (longest side opposite right angle)
⚡Live Interactive Quick Solver
Instant CalculationHypotenuse (c):5.00 units
Step: c = √(3² + 4²) = √(25) = 5.00
a^2 + b^2 = c^2
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🎯 Key Concepts
Understanding the triangle sides:
📐
c is the hypotenuseThe longest side, opposite the 90° angle
🔢
a and b are legsThe two sides that form the right angle
✓
Only for right triangles!This formula only works for 90° triangles
🎮 Interactive 60-Second Challenge
Test Your Speed: Pythagorean Theorem Blitz!
Calculate hypotenuse (c) and missing legs (a, b) under time pressure. Includes instant right triangle diagrams, classic 3-4-5 triples, and zero ads.
🔺 Find Hypotenuse (c = √(a²+b²))📐 Find Missing Leg (a, b)⚡ 3-4-5 & 5-12-13 Triples
🚀 Play Pythagorean Sprint Free→📝 Worked Examples
Find the Hypotenuse
Problem:
a = 3, b = 4. Find c.1
Write formula
a² + b² = c²2
Substitute
3² + 4² = c²3
Calculate
9 + 16 = 25 = c²4
Square root
c = √25 = 5Answer: c = 5
Find a Leg
Problem:
b = 5, c = 13. Find a.1
Rearrange
a² = c² - b²2
Substitute
a² = 13² - 5² = 169 - 253
Calculate
a² = 1444
Square root
a = √144 = 12Answer: a = 12
Is it a Right Triangle?
Problem:
Sides: 5, 12, 13. Right triangle?1
Check
Does 5² + 12² = 13²?2
Calculate
25 + 144 = 169 ✓3
Compare
169 = 169 ✓Answer: Yes! It's a right triangle.
💡 Pro Tips
3-4-5 and friends
Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
Double-check your c
c is ALWAYS the longest side (the hypotenuse)
Real-world use
Used in construction, navigation, and computer graphics
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