Right Triangle Calculator
Right Triangle - Solve mathematical problems with step-by-step solutions.
Right Triangle Calculator
Pythagorean Theorem & SOHCAHTOA
Enter any two values to solve the triangle.
Right Triangle Properties
This calculator uses the Pythagorean theorem (a² + b² = c²) and trigonometric functions (SOHCAHTOA) to solve for unknown sides and angles of a right-angled triangle.
How the Right Triangle Calculator Works
A right triangle is a triangle with one 90-degree angle. It has unique properties that make calculations straightforward using the Pythagorean theorem and trigonometric functions. The side opposite the right angle is called the hypotenuse, and it's always the longest side.
Key Components
- Pythagorean Theorem: a² + b² = c²
- Triangle Parts: Hypotenuse (c), Leg a (base), Leg b (height), Two acute angles
- Angle Sum: The two acute angles always add up to 90°
Key Formulas
Finding Sides
- Hypotenuse: c = √(a² + b²)
- Leg a: a = √(c² - b²)
- Leg b: b = √(c² - a²)
Finding Angles
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
Special Right Triangles
- 45-45-90 Triangle: Sides ratio: 1 : 1 : √2
- 30-60-90 Triangle: Sides ratio: 1 : √3 : 2
Real-World Applications
Construction & Architecture
Used to calculate roof slopes, stair dimensions, and ensure structures are square and level.
Navigation & Surveying
Calculate distances, heights, and angles for maps, GPS systems, and land measurements.
Frequently Asked Questions
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