Question 1204423

if

{{{b = 3.8}}}
{{{c = 5.9}}}
{{{gamma = 80}}}°


 use the Law of Sines:


{{{b/sin(beta)=c/sin(gamma)}}}

{{{3.8/sin(beta)=5.9/sin(80)}}}

{{{3.8sin(80)=5.9sin(beta)}}}

{{{sin(beta)=(3.8sin(80))/5.9}}}

{{{sin(beta)=0.6342829595671847}}}

{{{beta=sin^-1(0.6342829595671847)}}}

{{{beta=39.4}}}°


then

{{{alpha=180-(beta + gamma)}}}

{{{alpha=180-(39.4 + 80)}}}

{{{alpha=60.6}}}°



and side {{{a}}}


{{{a/sin(alpha)=c/sin(gamma)}}}

{{{a/sin(60.63)=5.9/sin(80)}}}

{{{a=(5.9/sin(80))sin(60.63))}}}

{{{a=5.22}}}