Law of Sines Calculator

Your details

Choose whether angles are in degrees or radians. All angle inputs and outputs follow this setting.
The law of sines always pairs a side with the angle directly across from it. Pick what you need to find.
A side whose length you know. Pick the unit that matches your problem.
The angle directly across from side a.
°
A second known angle, opposite the side you want to find.
°
Missing valueSingle solution
10.7784

The side length (in your chosen unit) or angle found by the law of sines.

Common ratio a / sin A12.4458m
Third angle C80
Third side c12.2567m
Side b (solved)10.7784m
Triangle area42.4585m²
Perimeter31.0351m
Inscribed circle radius (r)2.7362m
Circumscribed circle radius (R)6.2229m
Altitude from A to a (ambiguous check)6.9282m
Side b10.7784
Side c12.2567
Circumradius R6.2229
Inradius r2.7362

The missing side b measures about 10.7784 m.

  • The law of sines works whenever you have a side paired with its opposite angle (AAS, ASA, or SSA setup). The common ratio a/sin A equals the circumscribed circle diameter (2R).
  • Once one full side/sine ratio is fixed, every other side and angle in the triangle is determined by it.
  • No ambiguity: the given measurements pin down exactly one triangle.
  • The triangle has area 42.4585 m², inradius 2.7362 m, and circumradius 6.2229 m.

Next stepSwitch the mode to "missing angle" if instead you know two sides and one opposite angle.

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