Non-right triangle proofs

The  exercise appears under the Trigonometry Math Mission. This exercise helps to encourage understanding the Laws of Sines and Cosines. via their proofs.

Types of Problems
There is one type of problem in this exercise:


 * 1) Move the cards, prove the law: This problem presents a diagram of a non-right triangle and a plan of a proof to prove a trigonometric law. The student is expected to move the cards to present the correct steps to a proof of the law.Nrtp1.png

Strategies
Knowledge of the Law of Sines and Cosines, and their proofs, is encouraged beforehand to ensure success on this exercise.
 * 1) The law of Sines states $$ sin(A)/a=sin(B)/b=sin(C)/c$$.
 * 2) The law of Cosines stated $$ c^2=a^2+b^2-2abcos(C)$$.
 * 3) The proofs of these laws involve making right triangles by dropping altitudes and writing the altitudes in various ways to find relationships.

Real-life Applications

 * 1) The trigonometric rules themselves are a special case of Law of Sines and Law of Cosines, so these laws are more fundamental.
 * 2) The Pythagorean theorem can be viewed as a special case of the Law of Cosines.
 * 3) Trigonometry itself has several applications in physics regarding motion.