This week in Precal, we learned about the sine law and cosine law, as well as their formulas to solve problems. We also learned about when to use the sine law as well as the cosine law.

Sine Law

formula:

 

 

 

 

 

 

 

 

 

When determining either an angle or side length, we only need two equivalent fractions to solve in which there must be one complete fraction, and the other is partially complete to be able to solve for missing side length or angle.

Example 1: (Finding a side length)

 

 

 

 

 

 

Example 2: (Finding an angle)

 

 

 

 

 

 

 

Cosine law

formula

 

 

 

 

 

 

Determining the measure of a triangle with cosine law:

 

 

 

 

 

 

 

 

 

 

 

When to use cosine law and sine law (what’s their difference?)
Use Sine Law when there are two given angles and one side length, or there are two sides and an angle.

Use Cosine Law when there are three given side lengths, or two sides and the included angle. Remember: there has to be at least two given side lengths to be able to use cosine law.

you can use neither of the two laws when there are only three given angles and has NO given side length.