Right Triangle Calculator
Calculate the side lengths of a right triangle using the Pythagorean Theorem.
Geometry is not just for textbooks; it is the foundation of construction, architecture, and design. Our Right Triangle Calculator utilizes the Pythagorean Theorem to instantly compute the length of any missing side. Whether you are a student checking homework, a carpenter squaring a frame, or a designer planning a layout, this tool ensures your angles are right and your measurements are exact.
Sides (a² + b² = c²)
A = ?
B = ?
C = ?
Frequently Asked Questions
Mastering the Right Triangle
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.
1. 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" or a Pythagorean Triple.
2. 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).
- Ladders: To place a ladder safely against a wall (4:1 ratio generally), you calculate the base distance needed for the height you want to reach.
3. Frequently Asked Questions (FAQ)
Q: Does this work for all triangles?
No. This calculator only works for right-angled triangles (one angle is exactly 90 degrees). For other triangles, you must use the Law of Sines or Law of Cosines.
Q: What if I only know one side?
You cannot solve a triangle with only one side. You need at least two pieces of information (two sides, or one side and an angle).