A Different Proof of the Law of Cosines

  1. Draw circle B
  2. Draw any diameter DC
  3. Pick any point W
    and draw right triangle DCW
  4. Draw any diameter PQ
  5. Let the radius = a
  6. Let AB = c
  7. Let AC = b

Now complete the following proof:

8 AQ = ____________________ (in terms of a and c)
9
10 so, WC = ________________________
11 Then, WA = ______________________ (in terms of a, b, and )
12 Now, recall from geometry that ). Why? _______________________
13 Substituting in step 12,     (2a cos C)(b) = (        ) (         )
14 Simplifying step 13 and solving for c2, we obtain c2 = ____________________