Comparison of Law of Cosines, Law of Sines and Pythagorean Theorem

The law of cosines, law of sines and Pythagorean theorem are all very important parts of trigonometry. Firstly the Pythagorean theorem is very useful when finding the sides of a right triangle. All it takes is squaring side c and setting it equal to the sum of the squares of side a and b. The law of cosines is simply an extension of the Pythagorean theorem, this takes the Pythagorean theorem and subtracts 2(a)(b)cos(C) from the equation. This is very helpful when working with SAS and SSS triangles. When using the Law of cosines the triangle that you are using does not have to be a right triangle and also allows you to use an angle of the triangle to assist in finding its values. The Law of Sines is very helpful when working with AAS and ASA triangles because to use this you need two angles. All of these Laws and theorems are intertwined like a well oiled machine, and without one the whole machine will stop working.