Question 181607
<font size = 7 color = "red"><b>Edwin's solution using the law of sines:</font></b>
<pre><font size = 4 color = "indigo"><b>
{{{drawing(300,300,-3,9,-1,11,

triangle(0,0,7.3,0,-2.322883852,10.0346505),
locate(0,0,A), locate(7.3,0,B), locate(-2.3,10.5,C),
locate(4.5,1,"46.2°"), locate(2.9,-.3,c=7.3),locate(-.9,5,b=10.3)
 )}}}

Use the law of sines:

{{{matrix(1,5,a/sin(A),"=",b/sin(B),"=",c/sin(C))}}}

We are only dealing with the last two fractions:

{{{matrix(1,3,b/sin(B),"=",c/sin(C))}}}

Cross-multiply:

{{{matrix(1,3,b*sin(C),"=",c*sin(B))}}}

Divide both sides by {{{b}}}

{{{matrix(1,3,(b*sin(C))/b,"=",(c*sin(B))/b)}}}

{{{matrix(1,3,(cross(b)*sin(C))/cross(b),"=",(c*sin(B))/b)}}}

{{{matrix(1,3,sin(C),"=",(c*sin(B))/b)}}}

Substitute {{{7.3}}} for {{{c}}}, {{{matrix(1,1,"46.2°")}}} for {{{B}}},
and {{{10.3}}} for {{{b}}} and 

{{{matrix(1,3,sin(C),"=",(7.3*sin(46.2))/10.3)}}}

Now get your calculator,

{{{matrix(1,3,sin(C),"=",0.5115388024)}}}

Edwin</pre>