9-4 Law of Cosines :)

Law of Cosines is my favorite thing we've done so far in this chapter. It is used only when law of sines does not work.

There is just one formula that you have to use:

(Opposite leg)^2=(Adjacent leg)^2+(Other Adjacent leg)^2-2(Adjacent leg)(Other Adjacent Leg)COS(Angle Between)

Example 1

Solve the triangle:

a=8, b=5, C=60º

The first thing you need to do is draw a picture with what is given.

The second thing you need to solve for is c.

Using the formula, you get c^2=5^2+8^2-2(5)(8)Cos 60º

Solv for c, c=SquareRoot(5^2+8^2-2(5)(8)Cos 60º)

c=7

Now that you have c, you need to solve for the angles. I'm going to solve for angle A first.

Using the formula, you get 8^2=7^2+5^2-2(7)(5)CosA

A=Cos^-1((8^2-7^2-5^2)/(-2(7)(5)))

A=81.787º

Now to find angle B,

180º-81.787º-60º=38.213º

B=38.213º

----Carleyyy!