Ambiguous Case: Law of Sine

Two Triangles

One Triangle

None

Two Triangles

One Triangle

None

Two Triangles

One Triangle

None

$58\degree$ and $122\degree$

$61\degree$ and $119\degree$

$78\degree$ and $102\degree$

$74\degree$ and $106\degree$

$49\degree$

$29\degree$

$49\degree$ and $131\degree$

$29\degree$ and $151\degree$

no triangle possible

B = 11.219^o, C = 141.781^o, c = 19.078

B = 38.219^o, C = 114.781^o, c = 27.998

B = 11.219^o, C = 141.781^o, c = 19.078

OR

B = 38.219^o, C = 114.781^o, c = 27.998

no triangle possible

B = 14^o, C = 21^o, c = 8.7

B = 52^o, C = 102^o, c = 11.2

B = 52^o , C = 102^o, c = 11.2

OR

B = 128^o, C = 26^o, c = 5.0

 $A=67\degree,\ B=73\degree,\ a=5.7cm$  or  $A=33\degree,\ B=107\degree,\ a=3.5cm$  

 $A=65.4\degree,\ B=74.6\degree,\ a=5.7cm$  or  $A=34.6\degree,\ B=105.4\degree,\ a=3.5cm$  

Not a triangle

 $A=65.4\degree,\ B=74.6\degree,\ a=7cm$  or  $A=34.6\degree,\ B=105.4\degree,\ a=5cm$  

 $C=24\degree,\ B=15\degree,\ b=8m$ 

 $C=24\degree,\ B=15\degree,\ b=7m$ 

Not a triangle

 $C=30\degree,\ B=9\degree,\ b=7m$  

 $C=113\degree,\ A=36\degree,\ a=45.4cm$  or  $C=5\degree,\ A=144\degree,\ a=6.1cm$  

 $C=110.8\degree,\ A=38.2\degree,\ a=47cm$  or  $C=7.2\degree,\ A=141.8\degree,\ a=4cm$  

Not a triangle

 $C=110.8\degree,\ A=38.2\degree,\ a=45.4cm$  or  $C=7.2\degree,\ A=141.8\degree,\ a=6.1cm$