Triangle Calculator
Solve any triangle from three values (SSS, SAS, ASA, AAS, SSA) for all sides, angles, area, perimeter, and radii.
Solve a triangle
Enter any three values with at least one side. Leave unknowns blank.
Answer
Triangle solved
- Case: SSS (three sides)
- Sides: a = 7, b = 8, c = 9
- Angles: A = 48.1896851°, B = 58.41186449°, C = 73.3984504°
- Perimeter = 24
- Area = 26.83281573
- Inradius r = 2.236067977
- Circumradius R = 4.695742753
- Type: scalene, acute
How to use the triangle calculator
Enter any three measurements with at least one side and the solver finds every remaining side and angle using the Law of Sines, the Law of Cosines, and Heron's formula.
- Enter any three values (sides a/b/c and angles A/B/C), leaving unknowns blank.
- The solver detects the case (SSS, SAS, ASA/AAS, or SSA).
- It applies the Law of Sines or Cosines, then Heron's formula for the area.
- It also reports perimeter, inradius, circumradius, and the triangle type.
Formula or method
Law of Sines: a/sin A = b/sin B = c/sin C. Law of Cosines: c^2 = a^2 + b^2 - 2ab cos C.
Worked examples
SSS - three sides
Problem: a = 7, b = 8, c = 9
Solution: Angles A ≈ 48.19°, B ≈ 58.41°, C ≈ 73.40°; area ≈ 26.83.
SAS - two sides and included angle
Problem: a = 5, b = 7, C = 60
Solution: c = sqrt(25 + 49 - 2*5*7*cos 60) = sqrt(39) ≈ 6.24.
SSA - ambiguous case
Problem: a = 7, b = 10, A = 40
Solution: Two triangles exist because b sin A < a < b.