Pythagoras Theorem Solver
Solve right triangle problems using Pythagoras theorem with detailed step-by-step solutions
Right Triangle Calculator
Enter two side lengths of a right triangle to solve for the third
Theorem & Properties
Pythagorean Principle
In any right-angled triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Core Equation
a² + b² = c²
Where c is the hypotenuse, a and b are shorter legs.
Right Triangle Simulator
Real-time geometry and proofs without words
Pythagoras Theorem Formula
a² + b² = c²
Where: a and b are the legs, c is the hypotenuse of a right-angled triangle
Pythagoras Theorem Solver – Calculate Right Triangle Sides
Our Pythagoras Theorem Calculator helps you solve right triangle problems by calculating the missing side using the famous Pythagorean theorem. This essential geometry tool provides step-by-step solutions for educational and practical applications.
🔹 What is Pythagoras Theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. This fundamental relationship is expressed as:
a² + b² = c²
Where a and b are the legs (shorter sides) and c is the hypotenuse (longest side).
🔹 How to Use the Calculator
- Enter values for two sides of the right triangle
- Leave the side you want to calculate empty
- Click "Calculate Missing Side" to get the result
- Review the step-by-step solution provided
🔹 Features of Our Calculator
- Step-by-step calculation process
- Verification of the Pythagorean relationship
- Handles all three cases: solve for a, b, or c
- Precise decimal calculations
- Mobile-friendly and responsive design
- Educational tool with comprehensive information
🔹 Example Calculations
Example 1: Find hypotenuse (3-4-5 triangle)
Given: a = 3, b = 4, find c
c = √(3² + 4²) = √(9 + 16) = √25 = 5
👉 This is the famous 3-4-5 right triangle ✓
Example 2: Find missing leg
Given: a = 5, c = 13, find b
b = √(13² - 5²) = √(169 - 25) = √144 = 12
👉 This forms a 5-12-13 right triangle ✓
🔹 Applications of Pythagoras Theorem
- 🏗️ Construction: Building right angles, measuring distances
- 🗺️ Navigation: Calculating distances on maps
- 🏛️ Architecture: Designing structures with right angles
- 🎮 Computer Graphics: 3D modeling and game development
- 📐 Surveying: Land measurement and mapping
- ⚡ Physics: Vector calculations and force analysis
🔹 Frequently Asked Questions (FAQs)
Q1. What is a right-angled triangle?
A: A right-angled triangle has one angle that measures exactly 90 degrees. The side opposite this angle is called the hypotenuse.
Q2. Can Pythagoras theorem be used for non-right triangles?
A: No, Pythagoras theorem only applies to right-angled triangles. For other triangles, use the law of cosines.
Q3. What are some common Pythagorean triples?
A: Common triples include (3,4,5), (5,12,13), (7,24,25), and (8,15,17). These are sets of integers that satisfy a² + b² = c².
Q4. How accurate are the calculations?
A: Our calculator provides results with 4 decimal places of precision, suitable for most practical applications.
Q5. What if I enter invalid values?
A: The calculator will prompt you to provide exactly two side lengths. Make sure to leave one field empty for the side you want to calculate.
Academic & Scientific References
For further understanding and validation of the formulas used above, we recommend exploring these authoritative resources: