How do you use the law of cosines or law of sines if you are given a = 55, b = 25, c = 72?

1 Answer
May 22, 2015

The law of cosine is:

a^2=b^2+c^2-2bc cosalpha,

where alpha is the opposite angle of a (and so on for every angle of the triangle).

So:

cosalpha=(b^2+c^2-a^2)/(2bc)=(25^2+72^2-55^2)/(2*25*72)=0.773

cosbeta=(a^2+c^2-b^2)/(2ac)=(55^2+72^2-25^2)/(2*55*72)=0.957

cosgamma=(a^2+b^2-c^2)/(2ab)=(55^2+25^2-72^2)/(2*55*25)=-0.558.

So:

alpha~=39.37°

beta~=16.86°

gamma~=123.92°,

using the inverse function of the function y=cosx, that is y=arccosx.