Law of Cosines Calculator

This calculator applies the law of cosines to find the unknown side and all angles of a triangle when you know two sides and the included angle between them (the SAS configuration). The law of cosines states that c squared equals a squared plus b squared minus 2ab times cos(C), where a and b are the two known sides and C is the angle between them. This formula is a direct generalisation of the Pythagorean theorem and works for any triangle, acute, obtuse or right-angled. When C is exactly 90 degrees, cos(C) equals zero and the formula reduces to the familiar a squared plus b squared equals c squared. Once side c is found, the remaining angles can be obtained by applying the law of cosines again in rearranged form: cos(A) equals (b squared plus c squared minus a squared) divided by (2bc), and similarly for B. This calculator does all of that in one step. You enter side a, side b and angle C in degrees, and it returns side c, all three angles and the area of the triangle using the formula half times a times b times sin(C). Input values must all be positive and the angle C must be strictly between 0 and 180 degrees. The tool is useful for students working on NCEA geometry, engineers calculating diagonal dimensions across a known angle, and surveyors working with triangulated field measurements. For a triangle where two angles and a side are known, use the Law of Sines Calculator instead. Results are rounded to two decimal places; treat them as accurate for planning and checking purposes.

SAS mode: enter two sides and the included angle. All sides must be positive and angle C must be between 0 and 180 degrees.