Question 1085658

given: {{{A = 25}}} degrees, {{{a = 9cm}}}, and {{{c = 11cm}}}

The ambiguous case of the sine law, where two sides and one angle are given.


{{{a / sin(A) = c / sin(C) }}} if {{{A = 25}}} degrees,{{{ a = 9cm}}}, and {{{c = 11cm}}}, we have


{{{9cm / sin(25) = 11cm / sin(C) }}}


{{{9cm*sin(C) = 11cm *sin(25) }}}


{{{sin(C)  = (11cm/9cm) *sin(25) }}}


{{{sin(C) = 1.222222222222222 *0.42261826 }}}


{{{C =sin^-1(0.51653342888888879497372) }}}


{{{C =31.100006692833242512632}}}° 


{{{C =31.1}}}° 


{{{B=180-(25+31.1)=180-56.1=123.9}}}


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


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


{{{b=(9cm *sin(123.9) )/ sin(25)  }}}


{{{b=(9cm *0.830012 )/ 0.42261826  }}}


{{{b=7.470108cm / 0.42261826  }}}


{{{b=17.7cm}}}