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Pythagorean Theorem:
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The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This fundamental principle in geometry is attributed to the ancient Greek mathematician Pythagoras.
The calculator uses the Pythagorean Theorem formula:
Where:
Explanation: The theorem relates the lengths of the sides of a right triangle, allowing you to calculate any side if you know the other two.
Details: This theorem is fundamental in geometry and has practical applications in construction, navigation, physics, engineering, and computer graphics. It's essential for calculating distances and determining right angles in real-world scenarios.
Tips: Enter the lengths of both legs (sides a and b) in any consistent units (meters, feet, inches, etc.). The calculator will compute the hypotenuse length in the same units. Both values must be positive numbers.
Q1: Does this only work for right triangles?
A: Yes, the Pythagorean Theorem only applies to right-angled triangles. For other triangles, you would use different formulas like the Law of Cosines.
Q2: Can I calculate a leg if I know the hypotenuse and one leg?
A: Yes, you can rearrange the formula to \( a = \sqrt{c^2 - b^2} \) if you need to find one of the legs.
Q3: What units should I use?
A: You can use any units (meters, feet, inches, etc.) as long as both inputs are in the same units. The result will be in those same units.
Q4: Does this work in 3D space?
A: The theorem extends to three dimensions as \( d = \sqrt{a^2 + b^2 + c^2} \) for calculating space diagonals.
Q5: How accurate is this calculator?
A: The calculator provides results accurate to two decimal places, which is sufficient for most practical applications.