Law of sines and law of cosines word problems

The  exercise appears under the Trigonometry Math Mission. This exercise uses the laws of sines and cosines to solve applied word problems.

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


 * 1) Use trigonometry laws to solve the word problem: This problem provides a real-life situation in which a triangle is formed with some given information. The student is asked to correctly assess which law should be used, and then use it to solve the problem.Losalocwp1.png

Strategies
Knowledge of the laws of sines and cosines before doing this exercise is encouraged to ensure success, but the law of cosines can be derived from typical right triangle trigonometry using an altitude.
 * 1) The law of sines states $$ \frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c} $$. The a,b and c's can be interchanged.
 * 2) The law of cosines states $$ c^2=a^2+b^2-2abcosC $$.
 * 3) The law of sines is generally used in AAS, ASA and SSA triangles whereas the SSS and SAS triangles prefer the law of consines

Real-life Applications

 * 1) Trigonometry has many applications in physics as a representation of vectors.
 * 2) The problems in this exercise are real-life applications.