Expert: Sherman D. - 1/18/2005

Question
I did 20^2+15^2-2(20)(15)cosA=19^2 and got A=116 degrees;then I did 180-116=64 degrees as my final answer.What I did wrong was I did the supplement of one hundred and sixteen, but I want to know why that is wrong.In my bad diagram below where I illustrate what I did,the box should really look like a parallelogram with a resultant drawn.The resultant is 19 pounds;the resultant is the slashed lines.(This site doesn't allow me to make spaces therefore drawing the whole thing.)Therefore when they say find the angle between the 2 original forces, you want the angle ADC,right,so then to solve the problem,I found angle BCD(116 degrees) and did the supplement.What's wrong with that?
A_________B
 |      /|
15|   /   |
 |/      |
D---------C
  20pounds

Answer
20^2 + 15^2 - 2(20)(15)cosA = 19^2
400 + 225 - 600cosA = 361
625 - 600cosA = 361
-600cosA = -264
CosA = .44
A = 63.896°
A = 64°

Assuming 19 pounds was a given

The other angle is 116°

I would thank that it would be in reverse

-----------------------------------------------------------

Assuming 19 pounds wasn't a given, i tried it this way.

TanD = 15/20
(1/2)D = 36.87
D = 74°

(1/2)C = 53.13
C = 106°

When C and D are added together, you get 180° and as you know all the angles within a parallelogram add up to be 360°

If you could tell me what the answer is in the book and i figure out what problems either one of us might be having.