Question 1191140
i get:


angle A = 72 degrees.
a = 67.0


angle B = 78.2 degrees
b = 69


angle C = 29.8 degrees
c = 35


the sum of the angles is 180 degrees, as it should be.


the ratio of a / sine(A) = b / sine(B) = c/sine(C) is the same for all 3, as it should be.
that ratio was 70.482862 for all three.


the first thing i did was find the value of a using the law of cosines formula of:
a^2 = b^2 + c^2 - 2*a*b*cos(A).
the formula became:
a^2 = 69^2 + 35^2 - 2*69*35*cos(72) = 4493.447917
a = sqrt(4493.447917) = 67.03318519


once i got that, i was able to get the other values using the law of sines formula of:
a/sin(A) = b/sin(B) = c/sin(C)


a = 67.03318519
A = 72 degrees.


i got:
b = 69
B = 78.22636413 degrees.


and i got:
c = 35
C = 29.77363587 degrees.