Triangle Side & Angle Calculator: Solve Any Case
Table of Contents
Which formula should you use?
Use the law of sines when you know an angle-side opposite pair (ASA or AAS). Use the law of cosines when two sides and the included angle (SAS) or all three sides (SSS) are given. Our calculator switches formulas automatically once you enter the known values.
Triangle fundamentals
The sum of interior angles in any triangle is 180°. When solving for angles, subtract known values from 180° after you find missing sides.
Side lengths must satisfy the triangle inequality: the sum of any two sides must exceed the third.
Worked ASA, AAS, and SAS examples
ASA: Enter two angles and the included side. The calculator finds the third angle, then applies the law of sines to the remaining sides.
AAS: Provide two angles and a side opposite one of them. The workflow mirrors ASA once the missing angle is computed.
SAS: Input two sides and the included angle. The law of cosines yields the third side, then the law of sines finds the remaining angles.
SSS and the ambiguous SSA case
SSS: Use the law of cosines three times (or Heron’s formula for area) after confirming triangle inequality.
SSA: An angle opposite a known side can produce zero, one, or two valid triangles. The calculator flags multiple solutions when they exist.
Always check your calculator output against geometric intuition—if an angle reads >180°, re-evaluate your inputs.
Triangle problem-solving tips
- Sketch a quick diagram before you type values to reduce input mistakes.
- Round intermediate calculations to at least four decimals to preserve accuracy for the final answer.
- If you receive an error, confirm that side lengths obey the triangle inequality.
Practice with multiple triangle types
Once you understand which formula fits each case, triangle problems become routine. Keep a mix of classroom exercises and real-world applications handy so the patterns stick.