Consider a non-right triangle. a=39 b=25 c = 24.(a,b,c are the sides) Find A,B,C. (these are the degrees of the triangle)
I know theres an equation:
b^2= a ^2 + c^2 - 2accos(B)
and sinA/a = sinB/b = sinC/c
but when i do the problem i get
A= 74.55
B = 38.16
C = 36.68
but that doesnt make sense because the triangle should add up to 180 and 74.55+ 36.68 + 36.68 = 149.39
could there be two answers for each?..i thought that was only with not SSS what am i doing wrong?
When all 3 sides are given, we MUST use the Cosine Law.
I always find the largest angle, which will be opposite the largest side. The calculator will give me the correct angle directly without any further adjustment.
The problem arises using the Sine Law, where one of the remaining angles could be obtuse.
Since there can be only ONE obtuse angle, finding the largest angle with the Cosine Law takes care of that problem
I will test your answers:
39^2 = 25^2 + 24^2 - 2(25)(24)Cos A
cosA = -.266666..
A = 105.466° , already found your problem
by sine law
sinB/25 = sin105.66666/39
sin B=.6178..
B = 38.16° , you had that
so C = 180-38.16-105.47 = 36.37