Solving SSS triangles. Law of cosine is another formula used to find out the unknown side of the triangle. Solving an SSS by using the Law of Cosines is demonstrated here. We explain Solving an SSS Triangle with the Law of Cosines with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. We explain Solving an SSS Triangle with the Law of Cosines with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. The Laws of Sine and Cosine Objectives: Given a triangle and three quantities (ASA, SAS, SSS, SSA, AAS) of data about the triangle, use the law of sines, or the law of cosines to determine the three remaining unknowns. SSS and SAS. Also, to solve a triangle that is SSA (or side-side-angle) using the Law of Cosines, you have to be careful to find the correct triangle — … In either of these cases, it is impossible to use the Law of Sines because we cannot set up a solvable proportion. The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known. A proof of the Law of Cosines is given in Appendix A. The Law of Cosines is also sometimes called the Cosine Rule or Cosine Formula. To use the Law of Sines, you must know at least one side and its opposite anole. Law of Cosines • We can solve oblique triangles for SSS or SAS. Law of Cosines - SSS - Mr. C. Added Aug 1, 2010 by Mr. C. in Mathematics Use the Law of Cosines to find the measure of the angle C opposite the third side given sides a, b, and c. In this case, the Law of Sines isn’t an option. In such cases you can use the Law of Cosines. Law of Cosines The Law of Cosines works well for solving triangles when you have two sides and an angle, but the angle isn’t between the two sides. Explore the Law of Cosines with SSS given information through manipulating the triangle and observing changes in the equation and measures. The Law of Cosines relates the lengths of the sides of a triangle with the cosine of one of its angles. There is an alternate form of the Law of Cosines which is used to solve the SSS case. If we are given two sides and an included angle (SAS) or three sides (SSS) then we can use the Law of Cosines to solve the triangle i.e. If you are given three sides (SSS), or two sides and their included anzle (SAS), none of the ratios in the Law of Sines would be complete. • When given the lengths of all three sides of a Discussion Every triangle has three vertices and three sides. • If ABC is a triangle with sides a, b, and c, then we use For SAS For SSS • = + − 2 cos or cos = • = + − 2 cos or cos = • = + − 2 cos or cos = Example • Using the triangle shown at the right, find angle A. If the two sides and angles of the triangle are given, then the unknown side and angles can be calculated using the cosine law. Solving an SSS by using the Law of Cosines is demonstrated here. In the standard form of the Law of Cosines, each of the three equations is solved for the cosine of the angle to get $$\cos A = \dfrac{b^2 + c^2 - a^2}{2 bc }$$ $$\cos B = \dfrac{a^2 + c^2 - b^2}{ 2 ac }$$