A Different Proof
of the Law of Cosines
by Sydney H. Kung,
Jacksonville University
From Mathematics Magazine


  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 = _____


Send any comments or questions to: David Pleacher