Law of cosines

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

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


 * 1) Use the law of cosines 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 cosines to find the missing measurement and write it in the space provided.Lawofc1.png

Strategies
Knowledge of the law of 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 cosines states $$ c^2=a^2+b^2-2abcosC $$. The a,b and c's can be interchanged.
 * 2) The law of cosines is generally used on SSS and SAS triangles.
 * 3) To ensure simplicity, when using the law of cosines the largest angle should be found first (if there is an option).
 * 4) The law of cosines can be seen as a generalized Pythagorean theorem.

Real-life Applications

 * 1) Trigonometry has many applications in physics as a representation of vectors.
 * 2) Law of cosines can be used to calculate resulting speeds up airplanes and ships.
 * 3) The Pythagorean theorem can be "proved" from the law of cosines by assuming C is a right angle.