Triangle Calculator

Applies to both the angles you enter and the angles returned.
Only used when two sides and a non-included angle give two valid triangles.
Area
6
Triangle Solver
Side a
3
Side b
4
Side c
5
Angle A
36.869898
Angle B
53.130102
Angle C
90
Perimeter
12
Semiperimeter
6
Altitude to side a
4
Altitude to side b
3
Altitude to side c
2.4
Median to side a
4.272002
Median to side b
3.605551
Median to side c
2.5
Inradius
1
Circumradius
2.5
Classification by sides
scalene
Classification by angles
right
Case solved
SSS
Worked out from NIST Digital Library of Mathematical Functions, 4.15 Trigonometric identities and the solution of triangles and 2 other sources.

How this is worked out

4 steps
  1. Three sides known (SSS): each angle comes from the law of cosines.
  2. cos A = (b^2 + c^2 - a^2)/(2bc) = (4^2 + 5^2 - 3^2)/(2*4*5) -> A = 36.869898 deg
  3. Area by Heron: s = 6, A = sqrt(s(s-a)(s-b)(s-c)) = 6
  4. Sides a=3, b=4, c=5; angles A=36.869898, B=53.130102, C=90 degrees.

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