Right Triangle Calculator
Calculate missing sides, angles, area, and perimeter of right triangles using various input combinations. Perfect for trigonometry, geometry, and engineering applications.
Right Triangle Solver
Common Right Triangle Examples
Click on these links to see instant calculations with common right triangles:
Right Triangles
A right triangle has one 90-degree angle and follows the Pythagorean theorem. The relationships between sides and angles are governed by trigonometric ratios, making them fundamental in geometry and trigonometry.
Right Triangle Formulas
Area = (1/2) × base × height
Perimeter = a + b + c
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
Special Right Triangles
| Triangle Type | Angles | Side Ratios | Example |
|---|---|---|---|
| 45-45-90 | 45°, 45°, 90° | 1 : 1 : √2 | 1, 1, 1.414 |
| 30-60-90 | 30°, 60°, 90° | 1 : √3 : 2 | 1, 1.732, 2 |
| 3-4-5 | 36.87°, 53.13°, 90° | 3 : 4 : 5 | 3, 4, 5 |
| 5-12-13 | 22.62°, 67.38°, 90° | 5 : 12 : 13 | 5, 12, 13 |
| 8-15-17 | 28.07°, 61.93°, 90° | 8 : 15 : 17 | 8, 15, 17 |
- Construction: Calculate roof angles, building dimensions, and structural measurements
- Engineering: Analyze forces, design components, and solve mechanical problems
- Navigation: Determine distances, bearings, and elevation angles
- Physics: Resolve vectors, calculate projectile motion, and analyze wave properties
- Surveying: Measure land areas, heights, and distances using triangulation
Frequently Asked Questions
What is a right triangle?
A right triangle is a triangle with one 90-degree angle. It has three sides: two legs (adjacent to the right angle) and a hypotenuse (the longest side opposite the right angle).
How do you find the missing side of a right triangle?
Use the Pythagorean theorem (a² + b² = c²) for sides, or trigonometric ratios (sin, cos, tan) when you have an angle and one side. The method depends on what information you have.
What are the trigonometric ratios in a right triangle?
The three main ratios are: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent, where θ is one of the acute angles.