Q. Describe the Laws of Sines?

Ans.

Up to now we have dealt exclusively with right triangles.  The Law of Sines and the Law of Cosines are used to solve oblique triangles, triangles that do not contain a right angle.  To "solve a triangle" means to find the length of every side and the size of all three angles.  Given any three quantities (lengths of sides or angles) we want to find the remaining three quantities.  The Law of Sines is useful to solve ASA, AAS, and SSA triangles.  The Law of Cosines can be used to solve the other triangles, SSS and SAS.

Given a triangle abc, with angles α, β, γ, respectively, the law of sines states that

Notice how the sides and angles are labeled in the diagram.  The side labeled a is opposite to the angle α  Similarly, side b is opposite to angle β and side c is opposite to angle γ.

It is possible to derive the Law of Sines with your background knowledge.