ABC Triangle Calculator
Calculate all dimensions of a right triangle from any given measurements
Right Triangle Calculator
Enter any two sides
Triangle Results
Enter valid measurements to see triangle results
Make sure the values can form a valid right triangle
Example Calculations
Classic 3-4-5 Triangle
Given: Side a = 3, Side b = 4
Calculate: c = √(3² + 4²) = √(9 + 16) = √25 = 5
Angles: α = arctan(3/4) ≈ 36.87°, β = arctan(4/3) ≈ 53.13°
Area: A = (3 × 4) / 2 = 6 square units
Result: Perfect Pythagorean triplet (3, 4, 5)
45-45-90 Triangle
Given: Angle α = 45°, Side a = 5
Calculate: b = a = 5, c = a√2 ≈ 7.071
Special property: Isosceles right triangle
Area: A = (5 × 5) / 2 = 12.5 square units
30-60-90 Triangle
Given: Angle α = 30°, Side c = 10
Calculate: a = c/2 = 5, b = c√3/2 ≈ 8.660
Special property: Half of an equilateral triangle
Area: A = (5 × 8.660) / 2 ≈ 21.65 square units
Right Triangle Properties
Right Angle
One angle is exactly 90°
The largest angle in the triangle
Hypotenuse
Longest side opposite to right angle
Side c in our notation
Pythagorean Theorem
a² + b² = c²
Core relationship between sides
Quick Reference
Area = (a × b) / 2
Perimeter = a + b + c
Famous triplets: (3,4,5), (5,12,13), (8,15,17)
Special triangles: 30-60-90, 45-45-90
Understanding Right Triangles
What is a Right Triangle?
A right triangle is a triangle with one angle measuring exactly 90 degrees (π/2 radians). This special triangle has unique properties that make many calculations simpler and is fundamental in trigonometry and geometry.
The Pythagorean Theorem
The most important property of right triangles is the Pythagorean theorem: a² + b² = c², where c is the hypotenuse (longest side) and a, b are the two legs.
Pythagorean Triplets
Some right triangles have sides that are all integers. These are called Pythagorean triplets. The most famous is (3, 4, 5), but there are infinitely many such triplets.
Key Formulas
Pythagorean: a² + b² = c²
Area: A = (a × b) / 2
Perimeter: P = a + b + c
tan(α) = opposite / adjacent
sin(α) = opposite / hypotenuse
cos(α) = adjacent / hypotenuse
Applications
- •Construction and architecture
- •Navigation and GPS systems
- •Computer graphics and game development
- •Physics and engineering calculations