Pythagorean Theorem
Find the hypotenuse of a right triangle
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Non-linear Hypotenuse Relationship: The square of hypotenuse equals the sum of squares of legs (c = √(a² + b²)).
Variable Mechanics
Roles, constraints & impacts
Side A
Adjacent / Vertical Leg
Side B
Base / Horizontal Leg
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Non-linear Hypotenuse Relationship: The square of hypotenuse equals the sum of squares of legs (c = √(a² + b²)).
Common Mistakes & Traps
- Applying the formula to non-right triangles (only valid where one angle is exactly 90°).
- Incorrectly assuming c = a + b instead of taking the square root of their squares.
- Mixing up which side is the hypotenuse (c is always opposite the 90° angle and is the longest side).
Dimensional Analysis & Units
√([Length]² + [Length]²) = [Length] (linear distance)
Real-World & Industry Application
GPS triangulation, architecture framing, computer graphics screen diagonal calculations, and navigation waypoint vector distances.
Worked Example: Pythagorean Theorem
Given:
- a = 3
- b = 4
- c² = a² + b²
- c² = 3² + 4²
- c² = 9 + 16
- c² = 25
- c = 5
Answer: 5
Frequently Asked Questions
What is the Pythagorean Theorem formula?
c² = a² + b². Find the hypotenuse of a right triangle.
How do I calculate Pythagorean Theorem?
Enter Side A (a), Side B (b) into the calculator. It applies c² = a² + b² and shows every step of the working.
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