SSS Triangle Solver
Solve a triangle given all three sides
Enter Three Sides
Law of Cosines
cos(A) = (b² + c² - a²) / (2bc)
Triangle Diagram
Understanding SSS Triangles
When you know all three sides of a triangle (SSS), you can find all angles using the Law of Cosines. This case always has exactly one solution (if the sides satisfy the triangle inequality).
Solving SSS Triangles
- Check triangle inequality: Sum of any two sides must be greater than the third
- Use Law of Cosines to find angle A: cos(A) = (b² + c² - a²) / (2bc)
- Find angle B: cos(B) = (a² + c² - b²) / (2ac)
- Find angle C: C = 180° - A - B
Heron's Formula for Area
With three sides known, you can calculate area directly using Heron's formula:
Frequently Asked Questions
Why use Law of Cosines for SSS?
Law of Cosines directly relates all three sides to an angle. With SSS, we have all sides and need angles, making it the perfect tool.
Is there ever more than one solution?
No! SSS is unambiguous. If three sides satisfy the triangle inequality, there is exactly one triangle with those sides.
What is the triangle inequality?
The sum of any two sides must be greater than the third side. This must hold for all three combinations: a+b > c, a+c > b, b+c > a.
Which angle should I find first?
Any angle works, but finding the largest angle first (opposite the longest side) can help avoid rounding errors. Then use the formula for the second angle.
Can I use Law of Sines for SSS?
Not directly. Law of Sines needs at least one angle. Use Law of Cosines first to find an angle, then you can use Law of Sines if desired.
How do I verify my answer?
Check that all three angles sum to 180°. Also verify using Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) should all be equal.