Pythagorean Theorem Calculator
Find missing side lengths of right triangles
Calculated Missing Side Length
Understanding the Pythagorean Theorem
The Pythagorean Theorem Calculator helps you apply the fundamental theorem of Euclidean geometry concerning the three sides of a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
Formula: \(a^2 + b^2 = c^2\)
Where ‘a’ and ‘b’ are the lengths of the legs, and ‘c’ is the length of the hypotenuse.
How to Use the Pythagorean Theorem Calculator
To use the calculator, select what you wish to find:
- Find Hypotenuse (c): Enter the lengths of the two legs (a and b).
- Find Leg (a or b): Enter the length of the hypotenuse (c) and the length of one of the legs. The calculator will determine the length of the other leg.
Input your known values, click “Calculate Missing Side,” and get the result instantly!
Key Formulas Used
- To Find Hypotenuse (c): \[c = \sqrt{a^2 + b^2}\]
- To Find a Leg (a or b): \[a = \sqrt{c^2 – b^2}\] \[b = \sqrt{c^2 – a^2}\] (Ensure the hypotenuse ‘c’ is always longer than any leg)
Practical Applications of the Pythagorean Theorem
The Pythagorean theorem is widely used in various fields:
- Construction & Architecture: Ensuring structures are square (e.g., checking wall angles, roof pitches).
- Navigation: Calculating distances, especially in coordinate systems (e.g., in GPS, or determining shortest path).
- Engineering: Designing various components, from simple trusses to complex machinery, where right angles are involved.
- Art & Design: Used in perspective drawing and creating balanced compositions.
- Sports: For example, in baseball to calculate the distance from first base to third base.
Our Pythagorean Theorem Calculator simplifies these calculations, making it easier to apply this fundamental geometric principle.