Question 1076513
<b><pre>
Same as question 1076218

{{{drawing(400,950/3,-3,21,-3,16,
triangle(0,0,16,0,17.81953277,12.94664839),
red(arc(0,0,6,-6,0,36), arc(16,0,5,-5,82,180),
arc(17.81953277,12.94664839,7,-7,216,262)),
locate(7,0,c=16), locate(1,1,"36°"), locate(14.5,1.6,"98°"),
locate(17,7,"a=?"),locate(7,7,"b=?"),locate(16.3,11.5,"?°"),
locate(0,0,A),locate(16,0,B),locate(18,14,C))}}}

We find the third angle C by the fact that the three angles
of any triangle must have sum 180°.

 A  +  B  + C = 180°
36° + 98° + C = 180°  
     134° + C = 180°
            C = 46°

So we fill in angle C as 46°

{{{drawing(400,950/3,-3,21,-3,16,
triangle(0,0,16,0,17.81953277,12.94664839),
red(arc(0,0,6,-6,0,36), arc(16,0,5,-5,82,180),
arc(17.81953277,12.94664839,7,-7,216,262)),
locate(7,0,c=16), locate(1,1,"36°"), locate(14.5,1.6,"98°"),
locate(17,7,"a=?"),locate(7,7,"b=?"),locate(16,11.5,"46°"),
locate(0,0,A),locate(16,0,B),locate(18,14,C))}}} 

Next we use the law of sines:

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

We substitute what we know so far:

eq. 1:  {{{matrix(1,5,a/sin("36°"),""="",b/sin("98°"),""="",16/sin("46°"))}}}

Using the 1st and 3rd expressions of eq. 1:

{{{matrix(1,3,a/sin("36°"),""="",16/sin("46°"))}}}

Cross-multiply:

{{{matrix(1,3,a*sin("46°"),""="",16*sin("36°"))}}}

{{{matrix(1,5,a,""="",16*sin("36°")/sin("46°"),""="",13.07388251)}}}

Guess we'll just round that off to a = 13.1, and fill that in:

{{{drawing(400,950/3,-3,21,-3,16,
triangle(0,0,16,0,17.81953277,12.94664839),
red(arc(0,0,6,-6,0,36), arc(16,0,5,-5,82,180),
arc(17.81953277,12.94664839,7,-7,216,262)),
locate(7,0,c=16), locate(1,1,"36°"), locate(14.5,1.6,"98°"),
locate(17,7,"a=13.1"),locate(7,7,"b=?"),locate(16,11.5,"46°"),
locate(0,0,A),locate(16,0,B),locate(18,14,C))}}} 


Using the 2nd and 3rd expressions of eq. 1:

{{{matrix(1,3,b/sin("98°"),""="",16/sin("46°"))}}}

Cross-multiply:

{{{matrix(1,3,b*sin("46°"),""="",16*sin("98°"))}}}

{{{matrix(1,5,b,""="",16*sin("98°")/sin("46°"),""="",22.02615383)}}}

Guess we'll just round that off to b = 22.0  and fill that in:

{{{drawing(400,950/3,-3,21,-3,16,
triangle(0,0,16,0,17.81953277,12.94664839),
red(arc(0,0,6,-6,0,36), arc(16,0,5,-5,82,180),
arc(17.81953277,12.94664839,7,-7,216,262)),
locate(7,0,c=16), locate(1,1,"36°"), locate(14.5,1.6,"98°"),
locate(17,7,"a=13.1"),locate(6,7,"b=22.0"),locate(16,11.5,"46°"),
locate(0,0,A),locate(16,0,B),locate(18,14,C))}}}

And now we're done.

Edwin</pre>