Law Cosines Calculator

Area
6.000000
Law of Sines and Law of Cosines Triangle Solver
Side a
3.000000
Side b
4.000000
Side c
5.000000
Angle A
36.869898
Angle B
53.130102
Angle C
90.000000
Perimeter
12.000000
Semiperimeter (s)
6.000000
Circumradius (R)
2.500000
Inradius (r)
1.000000
Altitude to side a
4.000000
Triangle type
right scalene
Case solved
SSS
Law used
Law of cosines for each angle
Ambiguous (two triangles fit)
no
Worked out from Weisstein, Eric W. "Law of Cosines." MathWorld — c² = a² + b² − 2ab·cos C and 2 other sources.

How this is worked out

7 steps
  1. Three sides are known, so each angle comes from the law of cosines.
  2. cos A = (b² + c² − a²) / (2·b·c) → A = 36.869898°
  3. cos B = (a² + c² − b²) / (2·a·c) → B = 53.130102°
  4. cos C = (a² + b² − c²) / (2·a·b) → C = 90°
  5. Area = ½·a·b·sin C = ½ × 3 × 4 × sin 90° = 6
  6. Perimeter = 12; s = 6
  7. R = abc / (4·area) = 2.5; r = area / s = 1

Results are general information, not financial, tax, legal, medical or engineering advice.