SAS Triangle Calculator (Side-Angle-Side)

Your details

Length of the first side (adjacent to the included angle gamma).
Length of the second side (adjacent to the included angle gamma).
The angle between side a and side b. Must be between 0 and 180 degrees (exclusive).
deg
Side c
6.245

Third side, found via the Law of Cosines.

Side a5
Side b7
Angle alpha43.8979deg
Angle beta76.1021deg
Angle gamma60deg
Area15.1554
Perimeter18.245
Semiperimeter9.1225
Altitude h_a6.0622
Altitude h_b4.3301
Altitude h_c4.8536
Median m_a6.1441
Median m_b4.4441
Median m_c5.2202
Inradius r1.6613
Circumradius R3.6056

Triangle solved: third side c = 6.2450

  • This is a acute triangle.
  • The three angles are 43.90 deg, 76.10 deg, and 60.00 deg, totalling exactly 180 deg.
  • Area is 15.1554 square units; inradius 1.6613, circumradius 3.6056.
  • The circumradius (3.6056) is always at least twice the inradius (1.6613), satisfying Euler's inequality R >= 2r.

Next stepTo verify, apply the Law of Cosines in reverse using all three solved sides, or check that all angles sum to exactly 180 degrees.

 = Powered by OnlyCalculators