Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Law of sines... I don't get it

  1. Dec 8, 2017 #1
    1. The problem statement, all variables and given/known data

    Given is a triangle with sides a=3.1cm, b=5cm, c=4.7cm and opposite angle to side a, α=36°. I must find out for angles β and γ using the law of sines.

    2. Relevant equations

    Law of sines.

    3. The attempt at a solution

    I first tried:
    sin(γ)}/c=sin(α)/a ⇒ γ≈63.02°

    However, one could also calculate:
    sin(β)}/b=sin(α)/a ⇒ β≈71.45°

    Two approaches, that I believed to be equivalent, but which furnish different results. So, I obviously make something wrong. But ... I don't get it... what is it?
  2. jcsd
  3. Dec 8, 2017 #2


    User Avatar
    Science Advisor

    I think you have applied the law of sines correctly. The problem is that the triangle you have given is impossible. Try applying the law of cosines to the values you have given.
    Last edited by a moderator: Dec 8, 2017
  4. Dec 8, 2017 #3
    I draw the triangle on a piece of paper. What is wrong with this drawing?[​IMG]


    Attached Files:

  5. Dec 8, 2017 #4


    User Avatar
    Science Advisor

    Try measuring side a. If you look at it, side is is more like 3.0-3.1, not 3.7. This is also what the law of cosines would tell you.

    Edit: I see now that I misread your 3.1 as a 3.7. If you accept your values of 36 degrees, 5.0 and 4.7, then a must be 3.011. If you use this value, it all works out.
    Last edited: Dec 8, 2017
  6. Dec 8, 2017 #5


    User Avatar
    Science Advisor

    Note that once you have specified b, c, and alpha, this fixes the shape of the triangle. The other side and the other two angles are then determined. You can't make them whatever you want.
  7. Dec 8, 2017 #6
    Ahhh... now I see that.:mad: Of course, I first draw the triangle, then took the measures of all three sides and checked... but obviously that couldn't work that way. Thanks so much!:smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted