Question

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

Answer 1

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`.