Question 827223
<pre>
{{{drawing(400,160,-7,18,-2,8,

line(0,0,15,0),
line(15,0,-5.119388508,6.101049646),
line(0,0,-5.119388508,6.101049646),
locate(0,0,B), locate(15,0,C),locate(-5.4,7,A),
locate(3.8,4.5,b=15),locate(10,1,"24°"),
red(arc(15,0,13,-13,163,180),arc(-5.1194,6.10105,7,-7,310,342)),
locate(-3.5,5.15,"26°"), locate(6,0,"b=?"),locate(-4,3,"c=?"),
locate(0,1,"?°"),
red(arc(-5.1194,6.10105,8,-8,310,342),arc(0,0,4,-4,0,135),
arc(0,0,6,-6,0,135),arc(0,0,5,-5,0,135))


 )}}}

First we find &#8736;B 

  &#8736;A + &#8736;B + &#8736;C = 180°
24° + &#8736;B + 26° = 180°
      50° + &#8736;B = 180°
            &#8736;B = 130° 

{{{drawing(400,160,-7,18,-2,8,

line(0,0,15,0),
line(15,0,-5.119388508,6.101049646),
line(0,0,-5.119388508,6.101049646),
locate(0,0,B), locate(15,0,C),locate(-5.4,7,A),
locate(3.8,4.5,b=15),locate(10,1,"24°"),
red(arc(15,0,13,-13,163,180),arc(-5.1194,6.10105,7,-7,310,342)),
locate(-3.5,5.15,"26°"), locate(6,0,"b=?"),locate(-4,3,"c=?"),
locate(-.5,1.4,"130°"),
red(arc(-5.1194,6.10105,8,-8,310,342),arc(0,0,4,-4,0,135),
arc(0,0,6,-6,0,135),arc(0,0,5,-5,0,135))


 )}}}

Next we use the law of sines:

{{{a/sin(A)}}}{{{""=""}}}{{{b/sin(B)}}}{{{""=""}}}{{{c/sin(C)}}}

We fill in what we know:

{{{a/sin("26°")}}}{{{""=""}}}{{{15/sin("130°")}}}{{{""=""}}}{{{c/sin("24°")}}}

We use the first and second parts of the law of sines to find side "a":

{{{a/sin("26°")}}}{{{""=""}}}{{{15/sin("130°")}}}

Cross-multiply:

a·sin(130°) = 15·sin(26°)

Divide both sides by sin(130°)

{{{a}}}{{{""=""}}}{{{15sin("26°")/sin("130°")}}}

Use calculator

a = 8.583793357  (round as your teacher instructed, probably 8.6)

-----

We use the second and third parts of the law of cosines to find side "c":

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

{{{15/sin("130°")}}}{{{""=""}}}{{{c/sin("24°")}}}

Cross-multiply:

c·sin(130°) = 15·sin(24°)

Divide both sides by sin(130°)

{{{c}}}{{{""=""}}}{{{15sin("24°")/sin("130°")}}}

Use calculator

c = 7.964354681  (round as your teacher instructed, probably 8.0)

Edwin</pre>