Question 1207608
given:



{{{b=8}}}, {{{c=9}}}, {{{B =40}}}degrees


using law of sine:

{{{b/sin(B )=c/sin(C )}}}

{{{8/sin(40)=9/sin(C)}}}

{{{sin(C)=9sin(40)/8}}}

{{{sin(C)=0.7231360608973567}}}

{{{C=sin^-1(0.7231360608973567)}}}

{{{C=0.8083319666202583}}}

{{{C=46.314}}}
or
{{{C= 133.69}}}°


find third angle


{{{A=180-(40+46.314)=93.69}}}
or
{{{A=180-(40+133.69)=6.31}}}


side {{{a=(b/sin(B))*sin(A)}}}
{{{a=(8/sin(40))*sin(93.69)}}}
{{{a=12.42}}}

or
{{{a=(8/sin(40))*sin(6.31)}}}
{{{a=1.37}}}


Solution 1:


Sides:
{{{a = 12.42}}}
{{{b = 8}}}
{{{c = 9}}}

Angles:
{{{A = 93.69}}} °
{{{B = 40}}} °
{{{C = 46.314}}} °


Solution 2:


Sides:
{{{a = 1.37}}}
{{{b = 8}}}
{{{c = 9}}}

Angles:
{{{A = 6.31}}} °
{{{B = 40}}} °
{{{C = 133.69 }}}°