Using the Cosine Law

This week in math we learned how to use the cosine law when solving for an unknown angle.

First, we need to know when we would use the cosine law.   Unlike using the sine law, when we use the cosine law the angle that is given does not usually have a matching length.  As well as, when you use the cosine law there is usually only one angle given rather than two or three.

Our first step to using the cosine law is to know the formula.

Now, we have to put it to use in a equation.  So if this was our triangle:

With what is given in the equation, we just plot into our formula and change the variables if needed.  For our equation we changed the variable of A to Q, B to P, and C to R.  First, solve the square roots of 17 and 23 and then subtract 2(17)(23).  Next, we have to multiple it by Cos 72.  Finally, square each side of the equation so that we get q by itself.

Now, we have just solved for the side length of q.