Pythagorean Theorem Calculator
Find missing sides of right triangles using a² + b² = c². Perfect for students learning geometry with step-by-step solutions.
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Step-by-Step Solution
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Understanding the Pythagorean Theorem
What is the Pythagorean Theorem?
The Pythagorean Theorem is one of the most famous mathematical formulas, discovered by the ancient Greek mathematician Pythagoras around 500 BCE. It states that in a right triangle, the square of the hypotenuse (the longest side) equals the sum of squares of the other two sides.
Key Components
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Right Triangle: Must have one 90° angle
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Legs (a, b): The two sides that form the right angle
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Hypotenuse (c): The longest side, opposite the right angle
Common Applications
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Construction: Ensuring buildings and structures are square
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Navigation: Calculating shortest distances and routes
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Engineering: Designing ramps, roofs, and support structures
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Physics: Vector calculations and force analysis
How to Use It
Famous Example: 3-4-5 Triangle
Other Pythagorean Triples
Historical Context
While named after Pythagoras, this theorem was known to many ancient civilizations, including the Babylonians, Egyptians, and Indians, centuries before Pythagoras. The Egyptians used the 3-4-5 triangle to create right angles when building pyramids.
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