Yaaaay,cosines :D

Alright kiddie winks, today I'm going to teach you all about our friend the Law of Cosines :D

First off, you should know that this is sort of a last resort. Only use it when you can't do SOHCAHTOA or Law of Sines. The formula is somewhat lengthy, but make sure you know it because we have a quiz Tuesday.

Formula: opposite leg^2=adjacent leg^2+other adjacent leg^2-2(adjacent leg)(other adjacent leg)cos(angle between)

Now, who's ready for an example?!

Solve.

So for starters, we'll use our equation to find the third leg.

x^2=8^2+5^2-2(8)(5)cos60degrees

Square root both sides and plug the equation into your calculator like this:

square root of (8^2+5^2-2(8)(5)cos60degrees

Round to three decimal places.

You should get 7. Go back to your graph and fill this in on the remaining side.

Next, we use our equation to find another angle. We'll solve for angle A.

8^2=7^2+5^2-2(5)(7)cosA

Move all squares to one side then divide by -2(5)(7)

8^2-7^2-5^2/-2(5)(7)=cosA

Take the inverse and plug the following into your calculator:

cos-1((8^2-7^2-5^2)/(-2(7)(5))

Keep in mind that I am not using the ( ) for my health, you actually need them when plugging into your calculator.

Your answer should be 81.787 degrees. Fill that into your triangle.

To find the angle B, just subtract A and C from 180 degrees.

180-81.787-60= 38.213 degrees.

And that's that.

--Sarahhhhhhhhhhhhhhhhhhhhh