Section 8.2 - Law of Cosines

Hi, this section was about the law of cosines. Yay, fun.

Law of Cosines

The book says...
      Law of Cosines: the square of the length of any side of a triangle equals the sum of the squares of the lengths of the other two sides minus twice the product of the length of the other two sides and the cosine of the angle between them.

That pretty much means that...
       in any triangle ABC with sides a, b, and c...

     you generally use Law of Cosines with SAS or SSS

So, let's prove it.

We are given the oblique triangle ABC, 

To find the length of c, we use the distance formula.

Now, let's look at an example.

Area of a Triangle

To find the area of a triangle, you can use...

Unless you have a right triangle, getting the base and height can be a bit difficult so we were given three new equations for the area of a triangle. 

       Area of a triangle: is 1/2 the product of the lengths of any two sides of the triangle and the sine of the angle in between the two sides. 

We are given one more formula. Heron's formula, this is another way to find the area of a triangle

       Heron's formula: the area of a triangle with sides a, b, and c, is given by...

Yep, that was really fun. Hope it's helpful.

Carly