Question 1204594
<pre>
This is the ASS <font face="wingdings" size=4><b>J</b></font> case which can be solved by either the law of sines or the law
of cosines.  Both the other tutors used the law of sines, so for enrichment
purposes, I'll use the law of cosines, even though it's probably longer, but
it'll go straight to c, without the need to find an intermediate value.

{{{drawing(400,232000/657,-8.01,11.7,-1,15.4,
locate(0,0,alpha),locate(9.64,0,beta), locate(.4,1.3,116^o),
locate(-7.3,15.2,gamma),locate(-5,6,b=16),locate(1.5,8,a=22),
locate(5,0,c),

triangle(-7.013938349,14.38070474,0,0,9.635245763,0)  )}}}

{{{a^2}}}{{{""=""}}}{{{b^2+c^2-2*b*c*cos(alpha)}}}
{{{22^2}}}{{{""=""}}}{{{16^2+c^2-2*16*c*cos(116^o)}}}
{{{484}}}{{{""=""}}}{{{256+c^2-32*c*(-0.4383711468)}}}
{{{228}}}{{{""=""}}}{{{c^2+14.0278767c}}}
{{{0}}}{{{""=""}}}{{{c^2+14.0278767c-228}}}
{{{c^2+14.0278767c-228}}}{{{""=""}}}{{{0}}}
{{{c}}}{{{""=""}}}{{{(-(14.0278767) +- sqrt( (14.0278767)^2-4*(1)*(-228) ))/(2*(1)) }}}
{{{c}}}{{{""=""}}}{{{(-14.0278767 +- sqrt(1108.781325 ))/2 }}}
{{{c}}}{{{""=""}}}{{{(-14.0278767+- 33.2983682)/2 }}}
Since c cannot be negative, we use only the + sign.
{{{c = (19.2704915)/2 }}}
{{{c}}}{{{""=""}}}{{{9.63524575}}}

Edwin</pre>