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Online Pythagorean Theorem Calculator
Easily calculate any side of a right triangle using the Pythagorean theorem with this precise and user-friendly online calculator. Ideal for students, engineers, architects, and more.
RESULT
a = 3
A = 6
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What Is This Tool?
This calculator applies the Pythagorean theorem to find the length of one side of a right triangle when the lengths of the other two sides are known. It supports calculations for the legs and hypotenuse based on the formula a² + b² = c².
How to Use This Tool?
- Enter the lengths of any two known sides of the right triangle: a, b, or c
- Leave the side you want to calculate empty or set to zero
- Click the calculate button to compute the missing side length
- Review the displayed result to use in your geometry or design work
Key Features
- Calculates any side of a right triangle given the other two sides
- Uses the Pythagorean theorem formula and its rearranged forms
- Supports variables: leg a, leg b, and hypotenuse c
- Provides high-precision results with accurate square-root calculations
- Browser-based and easy to use without requiring downloads
Examples
- For a right triangle with legs a = 9 and b = 12, the hypotenuse c is calculated as c = √(9² + 12²) = 15
- Given hypotenuse c = 13 and leg b = 5, calculate leg a as a = √(13² - 5²) = √(169 - 25) = √144 = 12
- If hypotenuse c = 10 and leg a = 6, find leg b using b = √(10² - 6²) = √(100 - 36) = √64 = 8
Common Use Cases
- Solving right triangle side lengths in geometric problems
- Assisting in trigonometry studies and physics calculations
- Supporting construction measurements and architectural design
- Navigating and surveying distances involving right angles
- Designing objects and structures requiring precise side calculations
Tips & Best Practices
- Ensure that you input correct side lengths according to the right triangle properties
- Remember the hypotenuse (c) is always the longest side
- Use consistent measurement units for all sides entered
- Double-check inputs to avoid invalid entries that produce no real solutions
- Use the calculator for quick verification but cross-check complex problems manually when needed
Limitations
- Applicable only to right triangles with one 90-degree angle
- Does not compute real results if the hypotenuse is smaller than either leg
- Cannot solve triangles if insufficient side length information is provided
- Invalid inputs that violate triangle inequality rules will not yield valid outputs
Frequently Asked Questions
- What is the Pythagorean theorem used for in this calculator?
- The Pythagorean theorem relates the sides of a right triangle using the formula a² + b² = c² to calculate an unknown side length.
- Can I use this calculator for triangles that aren’t right angled?
- No, this tool works only for right triangles; it requires one 90-degree angle to apply the theorem correctly.
- What should I do if my inputs don’t produce a valid result?
- Check that the hypotenuse is the longest side and that the entered values obey triangle rules. Invalid inputs can produce no real numeric solution.
Key Terminology
- Leg
- One of the two sides that form the right angle in a right triangle, labeled as a or b.
- Hypotenuse
- The side opposite the right angle in a right triangle, labeled as c, and is the longest side.
- Pythagorean theorem
- A fundamental relation in geometry defined as a² + b² = c² connecting the sides of a right triangle.