Thursday, January 6, 2011

Law of Cosines

In 6.2 we learned about law of cosines.

From this triangle, we determined that:
sin A= y/c, therefore y= c * sin A
cos A= x/c, therefore x= c * cos A

From this information, we derived the law of cosines to be used with side-angle-side (SAS).





Finally, we learn the law of cosines for SAS:

Also, you can use this to find out b and c as well.


You can also use law of cosines with side-side-side (SSS).

We also learned about Heron's formula to figure out area. SSS is needed for this.

In Heron's formula, s is derived from the term "semi-perimeter" or half the perimeter. You determine s by:

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