Triangle Calculator
Find missing sides, angles, area, and perimeter of any triangle using known values.
Three Sides
About Triangle Calculator
- SSS: Calculate from 3 sides
- SAS: Calculate from 2 sides + included angle
- ASA: Calculate from 2 angles + included side
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How to Use This Calculator
- Select the calculation mode (SSS, SAS, or ASA) based on what information you know about the triangle
- Enter the known values: three sides for SSS, two sides and the included angle for SAS, or two angles and the included side for ASA
- Click Calculate to compute all triangle properties including area, perimeter, all sides, and all angles
- Verify the triangle inequality holds - the sum of any two sides must exceed the third side
Formula
SSS: Uses Heron's formula A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2. Angles found using Law of Cosines: cos(A) = (b²+c²-a²)/(2bc). SAS: A = (1/2)ab·sin(C), then use Law of Cosines for third side. ASA: Uses Law of Sines: a/sin(A) = b/sin(B) = c/sin(C).
Frequently Asked Questions
What is the triangle inequality theorem?▼
The sum of any two sides of a triangle must be greater than the third side. This ensures the three sides can actually form a triangle.
What's the difference between SSS, SAS, and ASA?▼
SSS (Side-Side-Side) uses three sides, SAS (Side-Angle-Side) uses two sides with the included angle between them, and ASA (Angle-Side-Angle) uses two angles with the included side between them.
Why do angles always sum to 180 degrees?▼
This is a fundamental property of Euclidean geometry. The internal angles of any triangle in a flat plane always add up to exactly 180 degrees.
What is Heron's formula?▼
Heron's formula calculates triangle area using only the three side lengths: A = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter (a+b+c)/2.