Radius of inscribed circle in the triangle, r = √ Triangle semi-perimeter, s = 0.5 * (a + b + c) Solving, for example, for an angle, A = cos -1 If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively then the law of cosines states:Ī 2 = c 2 + b 2 - 2bc cos A, solving for cos A, cos A = ( b 2 + c 2 - a 2 ) / 2bcī 2 = a 2 + c 2 - 2ca cos B, solving for cos B, cos B = ( c 2 + a 2 - b 2 ) / 2caĬ 2 = b 2 + a 2 - 2ab cos C, solving for cos C, cos C = ( a 2 + b 2 - c 2 ) / 2ab Solving, for example, for an angle, A = sin -1 Law of Cosines

If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively then the law of sines states: You could also use the Sum of Angles Rule to find the final angle once you know 2 of them. Use The Law of Cosines to solve for the angles. Given the sizes of the 3 sides you can calculate the sizes of all 3 angles in the triangle.

Use the Sum of Angles Rule to find the last angle SSS is Side, Side, Side Use The Law of Cosines to solve for the remaining side, bĭetermine which side, a or c, is smallest and use the Law of Sines to solve for the size of the opposite angle, A or C respectively. Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides you can calculate the sizes of the remaining 1 side and 2 angles. Sin(A) a/c, there are no possible trianglesĮrror Notice: sin(A) > a/c so there are no solutions and no triangle! use The Law of Sines to solve for the last side, bįor A a/c, there are no possible triangles.'.use the Sum of Angles Rule to find the other angle, B.use The Law of Sines to solve for angle C.Given the size of 2 sides (a and c where a c there is 1 possible solution Use The Law of Sines to solve for each of the other two sides. Given the size of 2 angles and the size of the side that is in between those 2 angles you can calculate the sizes of the remaining 1 angle and 2 sides. Use the Sum of Angles Rule to find the other angle, then Given the size of 2 angles and 1 side opposite one of the given angles, you can calculate the sizes of the remaining 1 angle and 2 sides. The total will equal 180° orĬ = π - A - B (in radians) AAS is Angle, Angle, Side Given the sizes of 2 angles of a triangle you can calculate the size of the third angle. Therefore, specifying two angles of a tringle allows you to calculate the third angle only. Specifying the three angles of a triangle does not uniquely identify one triangle.

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