Triangle+Trigonometry

 = Triangle Trigonometry by: Carolyn, Jordan & Isaac=

Triangle Trigonometry: There are three key formulas that you will need to know for solving this type of equations. Click here for a diagram: The law of cosines: c²=a²+b²-2ab(cos C) or cos C={a²+b²-c²__}__/ 2ab

The law of sines: __a__ = __b__ = __c__ sin A Sin B Sin C

and how to find the are of a triangle: K=1/2 ab(sin C)

Important Things- The important thing to know when doing a problem is to know what the information given is. If you have 2 sides and 1 corresponding angle of the side you need to realize that law of sines is necessary. When 2 sides are giving but not any of the corresponding angles of these sides are given then you need to realize that law of cosines is necessary. The given information determines what law you use to solve.

Summary- The point of these problems is to find all sides and angles of a triangle. Depending one what is given whether it is 2 sides and a angle or 2 angles of a side then you need to determine the law to use to find all the different sides and angles.

Common mistakes- When a angle is given between 2 given sides mistakes are usually made. When determining the other side and 2 angles 2 different triangles can be made. Once the other angles are found it is necessary to find the supplement as well. Both triangles are valid. There will be a 2 triangles with supplementary angles and different sized sides. People typically do not realize when two triangles are necessary. Try and solve these problems:  Q1) In triangle ABC, a=6, c-2 and mmedia type="youtube" key="m9Z3-_4iXgo" height="344" width="425" Copy the link into your web browser.  Law of Cosines lesson: http://www.youtube.com/watch?v=UaDdu4sdZXM Copy and paste the link into your browser.

Law of Sines: http://www.youtube.com/watch?v=PCZEJifjK4s&feature=related Copy and paste the link into your browser

 
Answers: Q1) 3.6 Q2) p=8