For your set-up side "a"=117; angle "β"=51°; "α"=39°; "γ" is the rt angle.

A set of formulas is: a/(sinα)=b/(sinβ)=c; the sin of a rt angle (γ)=1.

Given: 117/(sin39)=185.91="c".

Now you want side "b". Another formula is a^2+b^2=c^2; so: 185.91^2-117^2=20875^.5=144.482......km.