Right Triangle Calculator
Calculate angles, sides, area, perimeter, height, and other properties of a right triangle using any 2 known values. Enter any two values and get all other properties calculated automatically.
Calculation Results
| Property | Value |
|---|---|
| Side a (adjacent to angle β) | - |
| Side b (adjacent to angle α) | - |
| Side c (hypotenuse) | - |
| Angle α (opposite side a) | - |
| Angle β (opposite side b) | - |
| Area | - |
| Perimeter | - |
| Height (h) | - |
About the Right Triangle Calculator
This calculator provides a complete solution for right triangle calculations, allowing you to find all missing sides and angles when any two values are known. It implements the Pythagorean theorem and trigonometric functions to deliver accurate results.
How the Right Triangle Calculator Works
The calculator uses the following mathematical principles:
- Pythagorean theorem: a² + b² = c² where c is the hypotenuse
- Trigonometric functions: sin(α) = a/c, cos(α) = b/c, tan(α) = a/b
- Angle sum: α + β = 90° (since the right angle is 90° and all angles sum to 180°)
- Area calculation: Area = (a × b) / 2
- Perimeter calculation: Perimeter = a + b + c
- Height calculation: Height (h) = (a × b) / c
Understanding the Results
The calculator provides comprehensive information about your right triangle:
- Sides: The three sides of the triangle (a, b, and hypotenuse c)
- Angles: The two non-right angles (α and β) in degrees
- Area: The space enclosed by the triangle
- Perimeter: The total length around the triangle
- Height: The height relative to the hypotenuse
Practical Applications
Right triangle calculations are essential in many fields:
- Construction: Calculating roof pitches, stair angles, and structural components
- Navigation: Determining distances and bearings
- Physics: Resolving forces into components
- Engineering: Designing mechanical components and systems
- Surveying: Measuring land and creating maps