Question 139524
Given:
{{{b = 10}}}
{{{A = 35}}}°
{{{B = 68}}}°

Use:

{{{A+B+C=180}}}

{{{sin A/a = sin B/b = sin C/c}}}
  
{{{A+B+C=180}}}

{{{35+68+C=180}}}

{{{highlight(C=77)}}}


{{{sin A/a = sin B/b}}}

{{{sin A = a*sin B/b}}}

{{{sin A*b = a*sin B}}}

{{{  a = sin A*b /sin B}}}……. 

{{{sin A= sin 35= 0.57357643635105}}}..and 
{{{sin B= sin 68= 0.92718385456679}}}

{{{  a = 0.57357643635105*10 /0.93}}}……. 

{{{  a = 5.7357643635105/0.92718385456679}}}……. 

{{{  a = 5.7357643635105/0.92718385456679}}}……. 

{{{  a = 6.1862211418580329581605133296942}}}

{{{  highlight(a = 6.19)}}}

{{{sin B/b = sin C/c}}}……{{{sin C= sin 77= 0.97437006478524 }}}

{{{c*sin B = b*sin C}}}

{{{c = b*sin C/ sin B }}}……

{{{c = 10*0.97437006478524 / 0.92718385456679}}}

{{{c = 9.7437006478524 / 0.92718385456679}}}

{{{c = 10.508919670958861865272760329347}}}

{{{  highlight(c= 10.5)}}}