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Homework Help: Measure of the smallest angle in the triangle

  1. Aug 16, 2010 #1
    1. The problem statement, all variables and given/known data

    In a triangle, two sides that measure 6 centimeters and 10 centimeters form an angle that measures 80 degrees. Find to the nearest degree, the measure of the smallest angle in the triangle.

    2. Relevant equations

    A2 = B2 + C2 – 2bc Cos A

    3. The attempt at a solution

    I tried using this formula to get the answer but it didn't work out. This is one of the questions from the algebra 2 trigonometry regents. I know the answer which is 33 degrees but I dont know on how to get to that answer.
  2. jcsd
  3. Aug 16, 2010 #2
    Re: Trigonometry

    I think relevant equation would actually be

    [tex] \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} [/tex]

    along with the equation you've mentioned
  4. Aug 16, 2010 #3
    Re: Trigonometry

    Okay, then a = 6, b = 10 and C = 80 degrees, right? Then idk how to use the revelant equations you implied.
  5. Aug 16, 2010 #4
    Re: Trigonometry

    i just edited my reply. use your equation first and find c. Then use my equation to get A and B
  6. Aug 16, 2010 #5


    User Avatar
    Homework Helper

    Re: Trigonometry

    Can you show us your work? Because I was able to get the answer (approx 33.409°). Make sure you are in degree mode when doing your calculations (or convert the 80° to radians).

    Perhaps using the Law of Sines will work, but the OP may be required to use Law of Cosines for this problem.


    EDIT: Too slow ^.^
  7. Aug 16, 2010 #6
    Re: Trigonometry

    Thanks a lot praharmitra for this. I really appreciate it.
  8. Aug 16, 2010 #7


    User Avatar
    Science Advisor
    Homework Helper

    Re: Trigonometry

    Actually, if you're not sure about the sine law, you can solve it using sin, cos and tan in right-angled triangles (draw the triangle, call its height h and relate it to the sine of 80 degrees, then divide the side of length 10 into two pieces of length L and 10 - L and relate L to the cosine of 80 degrees).
  9. Aug 16, 2010 #8
    Re: Trigonometry

    first you need to find side c using cosine law c2=a2 +b2=2abcosC
    then use sine law to find angle A, cause the higher angle, the longer the side, since side A is the shortest, which means angle A is the smallest.
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