You can put this solution on YOUR website! First, the lower case letters represent the lengths of sides. "a" is the side opposite angle A, "b" is the side opposite angle B and "c" is the side opposite angle C. So the measures of "b" and "c" are not degrees.
Starting with two sides and an angle and looking for the third side is a job for the Law of Cosines. (Why? The Law of Cosines has all three sides and an angle in it. And in general, if you know all but one the variables in an equation you can use the equation to solve for the missing variable. So the Law of Cosines could also be used if you had all three sides and wanted to find an angle.)
The version of the Law of Cosines that has a, b, c and A in it is:
Substituting in the given values:
Now we solve for a. We start by simplifying the right side. Since functions are at the level of the "P" in PEMDAS, we will start with cos(15):
Next, exponents:
Next multiplication:
And last, addition and subtraction:
To solve for "a" we now just need to find the square root of each side. (Since "a" represents the length of a side of a triangle and since the length cannot be negative, we will reject/ignore the negative square root.)
a = 8.03354363
(