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. SSS and SAS. Law of Cosines 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. 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. If the two sides and angles of the triangle are given, then the unknown side and angles can be calculated using the cosine law. 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 — … • When given the lengths of all three sides of a The Law of Cosines is also sometimes called the Cosine Rule or Cosine Formula. In this case, the Law of Sines isn’t an option. Solving SSS triangles. In such cases you can use the Law of Cosines. A proof of the Law of Cosines is given in Appendix A. 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. 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. Law of Cosines • We can solve oblique triangles for SSS or SAS. 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. Solving an SSS by using the Law of Cosines is demonstrated here. 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. Discussion Every triangle has three vertices and three sides. Law of cosine is another formula used to find out the unknown side of the triangle. To use the Law of Sines, you must know at least one side and its opposite anole. In either of these cases, it is impossible to use the Law of Sines because we cannot set up a solvable proportion. In the standard form of the Law of Cosines, each of the three equations is solved for the cosine of the angle to get \(\cos A = \dfrac{b^2 + c^2 - a^2}{2 bc }\) \(\cos B = \dfrac{a^2 + c^2 - b^2}{ 2 ac }\) 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 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. 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. • 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.

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