Right Triangle Calculator
Solve right triangles and calculate all sides, angles, area, and perimeter
Right Triangle Calculator
Enter any 2 values (sides or angles) to solve the right triangle. Leave other fields empty.
Sides
Angles
Example Calculations
3-4-5 Right Triangle
Given: a = 3, b = 4
Calculate: c = √(3² + 4²) = √(9 + 16) = √25 = 5
Area: ½ × 3 × 4 = 6
Perimeter: 3 + 4 + 5 = 12
Using Angle and Side
Given: c = 10, angle A = 30°
Calculate: a = c × sin(30°) = 10 × 0.5 = 5
Calculate: b = c × cos(30°) = 10 × 0.866 = 8.66
Angle B: 90° - 30° = 60°
Right Triangle Properties
One angle is exactly 90°
Hypotenuse is the longest side
Follows Pythagorean theorem: a² + b² = c²
Two acute angles sum to 90°
Area = ½ × leg₁ × leg₂
Common Right Triangles
Quick Formulas
Understanding Right Triangles
What is a Right Triangle?
A right triangle is a triangle where one angle is exactly 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse and is always the longest side. The other two sides are called legs or catheti.
Pythagorean Theorem
The fundamental relationship in right triangles is the Pythagorean theorem: a² + b² = c², where a and b are the legs and c is the hypotenuse. This theorem allows us to find any missing side when two sides are known.
Trigonometric Ratios
sin(A) = opposite/hypotenuse = a/c
cos(A) = adjacent/hypotenuse = b/c
tan(A) = opposite/adjacent = a/b
Special Right Triangles
- 45-45-90 triangle: Legs are equal, hypotenuse = leg × √2
- 30-60-90 triangle: Sides in ratio 1 : √3 : 2