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Law of sines

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Given triangle ABC with the measure of angel A = 60 degrees, the length of BC = sq rt of 3, and the length of AC = 1/5. How many soulutions are there for the measure of angle B?

    3. The attempt at a solution
    1. sin(60) / sq rt 3 = sinB / (1/5)

    2. sq rt 3 / 2 * 1 / sq rt 3 * 5

    3. 5/2 = sin(B)
    = Undefined because domain is [-1,1]

    It would seem I did something wrong but I keep getting the same thing, any assistance would be great.
     
  2. jcsd
  3. Apr 24, 2009 #2

    danago

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    Gold Member


    2. sq rt 3 / 2 * 1 / sq rt 3 * 5


    Should be:


    2. sq rt 3 / 2 * 1 / sq rt 3 * (1/5)


    You have just made an arithmetic mistake.
     
  4. Apr 24, 2009 #3
    So if angle B is 5.74 degrees how would you go about finding how many solutions there are? Originally I tried seeing how many times 5.8 went into 90 but I decided that couldn't be right so I started to subtract it from 180 degrees and see if it fit in the domain of arcsin. Which also seems to have provided the wrong answer :(. If the answer were undefined would the number of solutions be zero?
     
  5. Apr 24, 2009 #4
    This is the ambiguous case for the Law of Sines -- A S S. ;)

    I think you're going about this the wrong way -- I'm not sure you're supposed to find angle B. First, draw a diagram (hint: make AB the base of the triangle). Drop a perpendicular from C to side AB -- this is the height of the triangle (h). How would you go about finding h?


    01
     
  6. Apr 25, 2009 #5
    Well assuming that is possible and setting AB as base ( I am not sure how that is assigned the base ) I get..

    1. Angle A = 60 Angle B = 5.74 therefore Angle C = 114.26
    2. Draw perpendicular and if base is DE now in triangle DEF then Angle F is 57.13
    3. 180 - (57.13 + 90 = 147.13) = 32.87 Therefore Angle E is 32.87
    4. sin(32.87)= X / sq rt 3 Thus X(h) = 0.94
    5.Then from that use a2+b2=c2 to get 1/2 base which ended up being 0.92 so base = 1.84
    6.AB = 1.84

    Well the problem is I do not know how to find the number of solutions from this either ;/.

    The answer is either 0,1,2,3, or can not be determined as I as I already missed it with none of the above. =/ It would seem about 60% of time the answer is two but its not very helpful for when its not lol
     
  7. Apr 25, 2009 #6
    I'm not sure what you did ^ up there. Can you draw a diagram and post it here?

    I don't think you got the height of the triangle (h as I defined it). Hint: the way to find h doesn't involve the Law of Sines at all.


    01
     
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