Triangle Calculator
Solve any triangle - find missing sides, angles, area, and perimeter
Triangle Solution
Select input type and enter values to solve the triangle.
Related Math Calculators
How to Use the Triangle Calculator
- SSS (Side-Side-Side): Enter all three side lengths
- SAS (Side-Angle-Side): Enter two sides and the included angle
- ASA (Angle-Side-Angle): Enter two angles and the included side
- AAS (Angle-Angle-Side): Enter two angles and any side
- SSA (Side-Side-Angle): Enter two sides and an angle opposite one of them
Example: For a triangle with sides 3, 4, 5 (SSS), the calculator will find all angles and calculate area = 6 and perimeter = 12.
Triangle Solving Methods
Triangles can be solved using various methods depending on the known information. Our calculator uses the law of sines and law of cosines to find missing measurements.
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines
c² = a² + b² - 2ab·cos(C)
Triangle Area Formulas
- Using base and height: Area = ½ × base × height
- Using two sides and included angle: Area = ½ × a × b × sin(C)
- Using Heron's formula: Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2
Real-World Applications
- Construction: Roof trusses, structural design
- Navigation: GPS triangulation, surveying
- Engineering: Force analysis, mechanical design
- Astronomy: Distance measurements, satellite positioning
Triangle Types
- Acute Triangle: All angles less than 90°
- Right Triangle: One angle equals 90°
- Obtuse Triangle: One angle greater than 90°
- Equilateral Triangle: All sides and angles equal
- Isosceles Triangle: Two sides and two angles equal
- Scalene Triangle: All sides and angles different