Triangle Calculator
Calculate triangle properties including area, perimeter, angles, and sides using different methods.
Triangle Calculator
Calculate triangle properties using different methods
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Results
Triangle properties and visualization
Area
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Perimeter
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Sides
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Angles
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Triangle Formulas
Area
Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2
Law of Cosines
c² = a² + b² - 2ab·cos(C)
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Triangle Inequality
The sum of the lengths of any two sides must be greater than the length of the remaining side.
Understanding Triangle Calculations
Triangle Calculation Methods
There are several methods to calculate triangle properties based on the information you have:
- SSS (Side-Side-Side): When you know all three sides of a triangle. This method uses Heron's formula for area and the Law of Cosines for angles.
- SAS (Side-Angle-Side): When you know two sides and the included angle. The area can be calculated using A = (1/2)ab·sin(C).
- ASA (Angle-Side-Angle): When you know two angles and the included side. The third angle can be found since the sum of angles is 180°, and the other sides can be found using the Law of Sines.
- AAS (Angle-Angle-Side): When you know two angles and a non-included side.
- SSA (Side-Side-Angle): When you know two sides and a non-included angle. This case may have zero, one, or two solutions.
Special Triangles
Equilateral Triangle
All sides and angles are equal.
- All sides are equal
- All angles are 60°
- Area = (√3/4) × s²
Isosceles Triangle
Two sides and two angles are equal.
- Two sides are equal
- Two angles are equal
- Height bisects the base
Right Triangle
One angle is 90° (right angle).
- Follows Pythagorean theorem: a² + b² = c²
- Area = (1/2) × base × height
Applications of Triangle Calculations
Triangle calculations are used in various fields:
- Architecture and construction for roof designs and structural stability
- Land surveying and navigation
- Computer graphics and game development
- Physics for force vector calculations
- Astronomy for calculating distances between celestial bodies