Question 1131840

solve triangle with: 
{{{a=7.5}}}
{{{c=2.3}}}
{{{B=14.1 }}}° 
 
use the Law of Cosines to find side {{{b}}}

{{{b=sqrt(a^2+c^2-2ac*cos(B))
{{{b=sqrt(7.5^2+2.3^2-2*7.5*2.3*cos(14.1))}}}
{{{b=sqrt(56.25+5.29-34.5*0.969872)}}}
{{{b=sqrt(61.54-33.460584)}}}
{{{b=sqrt(28.079416)}}}
{{{b=5.2990014}}}
{{{b=5.299}}}

use the Law of Sines to find angle {{{C}}}

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

{{{2.3/sin(C)=5.299/sin(14.1)}}}
{{{2.3/sin(C)=5.299/0.243615}}}
{{{2.3/sin(C)=21.751534183034706}}}
{{{sin(C)=2.3/21.751534183034706}}}
{{{sin(C)=0.10573966786186073039109207653681}}}
{{{C=sin^-1(0.10573966786186073039109207653681)}}}
{{{C=6.07}}}°

and use the sum of the angles in triangle to find angle {{{A}}}

{{{A=180-(14.1+6.07)}}}°
{{{A=180-20.7}}}°
{{{A=159.93}}}°