Week 15: Law of Sines and Cosines

Coming back from Thanksgiving break, we only had one more chapter till the end of this semester. We began this week on chapter 5: Triangle Trigonometry.

We looked at the Law of Sines and Cosines this week.

Law of Sines:
Law of sines is using sines of course.

The equation:

 sin A    sin B     sin C
------ = ------ = ------
   a          b          c

When do you use sine?
1. when there are two sides and one opposite angle: has two possible solutions
2. when there are two angles and one opposite side: has one possible solution

How do you solve this?
1. Find one side and its angle
2. Find another that either has one side or angle
3. make them equal to each other like the equation above.
4. Solve.

Below is one example of how to solve a law of sines problem.

There is an element that you can have more than one solution. The reason behind it is because there might be another answer on a different angle on the unit circle.

Law of Cosines:

a^2=b^2 + c^2 - 2bccosA

b^2=a^2 + c^2 - 2accosB

b^2=a^2 + b^2 - 2abcosC

This is the equations used to solve Law of Cosines.

When do you use Law of Cosines?

1. When all the sides are known but no angles

2. When there are two sides and an enclosed angle and you have to try to find the opposite angle.

a Law of Cosines problem is one type of problem that may go back to Law of sines to finish an equation unless law of cosines is wanted to be used. 

To solve it, you just plug in what is necessary and then you solve for what is being solved. 

This is what we covered for Law of SInes and Cosines.

SEE YOU NEXT WEEK!