Question 930722

The three angles in triangle always add to {{{180}}}.° 
If {{{A=alpha= 40}}} degrees {{{B = 60}}} degrees, angle of {{{C=180-(40+60)=180-100=80}}}degrees; so,you have a Scalene Triangle: no equal sides,
no equal angles  

use Law of Sines:

{{{sin (alpha )/a=sin (beta) /b= sin (gamma )/c}}}
 
	 
if {{{b = 30}}}, {{{alpha= 40}}}, {{{beta = 60}}}, then


{{{sin (40 )/a=sin (60) /30}}}...cross multiply


{{{30*sin (40 )=a*sin (60)}}}


{{{30*0.64278761=a*0.8660254}}}


{{{19.2836283=a*0.8660254}}}


{{{19.2836283/0.8660254=a}}}


{{{a=22.27}}}



{{{sin (60) /30= sin (80 )/c}}}

{{{c*sin (60)= 30*sin (80 )}}}

{{{c= (30*sin (80 ))/sin (60)}}}

{{{c= (30*0.984807753)/0.8660254}}}

{{{c= 34.12}}}