Right Triangle Calculator

The right triangle is one of the most important shapes in geometry and construction. Its unique properties, governed by the Pythagorean Theorem, allow us to calculate unknown distances with incredible precision using just a few known measurements.

The Pythagorean Theorem (a² + b² = c²)

This famous formula states that for any right-angled triangle, the square of the hypotenuse (the long side opposite the right angle) is equal to the sum of the squares of the other two sides.

Example: If one side is 3 and the other is 4:
3² + 4² = 9 + 16 = 25.
The square root of 25 is 5. So the hypotenuse is 5.
This is known as the "3-4-5 Triangle".

Practical Uses

• Construction: Builders use the 3-4-5 rule to ensure corners of a room or deck are perfectly "square" (90 degrees). If measurements don't match this ratio, the walls are crooked.
• Navigation: If you travel 10 miles North and 10 miles East, the straight-line distance back to your start is the hypotenuse of that triangle (approx 14.1 miles).
• Graphics & Gaming: 3D rendering engines rely heavily on calculating triangle properties to draw realistic scenes and calculate lighting.