anonymous
  • anonymous
Find m∠B, given a = 11, b = 12, and c = 17. I used the law of cosines to get cos(b) = (11^2 - 12^2 + 17^2) / (2 * 11 * 17) which is equal to 40.75 degrees but that is not in my answer list. These are the ones I can choose: m∠B = 49.9º m∠B = 40.1º m∠B = 45.3º m∠B = 44.7º
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Oops. Wrong answer. Let me repost it.
anonymous
  • anonymous
Here: cos(b) = (11^2 - 12^2 + 17^2) / (2 * 11 * 17)
phi
  • phi
the convention is angle B is opposite side b. the law of cosines for this problem is b^2 = a^2 + c^2 - 2 a c cos(B) 12^2 = 11^2 + 17^2 - 2*11*17*cos(B) now solve for cos(B) 12^2 - 11^2 -17^2 = -2*11*17*cos(B) cos(B)= (11^2 +17^2-12^2)/(2*11*17) that looks like your formula. what did you get for an answer ?

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phi
  • phi
cos(B) = 0.711 B= acos(0.711) type into google acos(0.711) in degrees=
anonymous
  • anonymous
But by the information on this page (http://mathworld.wolfram.com/LawofCosines.html) the minus sign should be in front of the b^2. That is what's confusing me.
anonymous
  • anonymous
So shouldn't it be cos(B) = (11^2 - 12^2 + 17^2) / (2 * 11 * 17)
anonymous
  • anonymous
Ah. I was typing the question into Wolfram Alpha and it said B was equal to 40.75 degrees. Why didn't it solve it correctly?
phi
  • phi
you have 12^2 = 11^2 + 17^2 - 2*11*17*cos(B) you could write this as 12^2 - 11^2 - 17^2 = -2*11*17*cos(B) and cos(B)= (12^2 - 11^2 - 17^2)/(-2*11*17) or you could start with 12^2 = 11^2 + 17^2 - 2*11*17*cos(B) add 2*11*17*cos(B) to both sides: 2*11*17*cos(B) + 12^2 = 11^2 + 17^2 and 2*11*17*cos(B) = (11^2 + 17^2 - 12^2) and cos(B) = (11^2 + 17^2 - 12^2)/(2*11*17) which is the same as the first expression, except top and bottom have been multiplied by -1 both expressions give the same answer.
anonymous
  • anonymous
I got the correct answer now which is 44.68 degrees.

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