Law of sines

The  exercise appears under the Trigonometry Math Mission. This exercise introduces the law of sines as a way to solve general (not necessarily right) triangles.

Types of Problems
There are two types of problems in this exercise:


 * 1) Use the law of sines to solve the triangle: This problem provides a labeled triangle and a missing side or angle. The student is expected to use the law of sines to find the missing measurement and write it in the space provided.
 * 2) Use the law of sines to find the correct triangle: This problem provides a labeled triangle and a missing side or angle. The student is expected to use the law of sines and the given type of triangle to correctly determine which triangle in this ambiguous case provides the correct measurement. They will then write it in the space provided.

Strategies
Knowledge of the law of sines 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 cosines states $$ \frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c} $$. The a,b and c's can be interchanged.
 * 2) The law of sines is generally used on ASA and AAS triangles.
 * 3) To ensure simplicity, when using the law of sines the smallest angle should be found first (if there is an option).
 * 4) Using the law of sines on an SSA triangle is an ambiguous case in which there can be one, none, or two solutions. The problems from this exercise will tell the student is the acute or obtuse triangle is needed

Real-life Applications

 * 1) Trigonometry has many applications in physics as a representation of vectors.
 * 2) Law of sines can be used to calculate resulting speeds up airplanes and ships.