Given&nbsp;b=2,&nbsp;a=3, and&nbsp;B=40&nbsp;(degrees), determine whether this information results in one triangle, two triangles, or no triangle at all. Any resulting triangles should be resolved.

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Given&amp;nbsp;b=2,&amp;nbsp;a=3, and&amp;nbsp;B=40&amp;nbsp;(degrees), determine whether this information results in one triangle, two triangles, or no triangle at all. Any resulting triangles should be resolved.

oces3y · Accepted Answer

Step 1  Given thet, the values are b=2, a=3 and B=40∘  Recall that, the sine formula is asin⁡A=bsin⁡B=csin⁡c  sin⁡Aa=sin⁡Bb  sin⁡A=a(sin⁡Bb)  A=sin−1(a×sin⁡Bb)  Step 2  Substitute a=3, b=2 and B=40∘ in A=sin−1(a×sin⁡Bb)  A=sin−1(3×sin⁡(40∘)2)  =sin−1(0.9642)  =1.3023×180∘π  =74.6162∘  A=74.6∘  or  A=180∘−74.6∘  A=105.4∘   (∵105.4∘+40∘&amp;lt;180∘)  Step 3  Let A=74.6∘ then the angle of C is,  C=180∘−74.6∘−40∘  Use the sine formula to find the value of c.  sin⁡Bb=sin⁡Cc  c=bsin⁡Csin⁡A  c=2sin⁡65.4∘sin⁡40∘  c=2.83  Thus, the possible values of the triangle is  a=3, b=2, c=2.83 and A=74.6∘, B=40∘, C=65.4∘  Step 4  Let A=105.4∘ then the angle of C is,  C=180∘−105.4∘−40∘  =34.6∘  Use the sine formula to find the value of c.  sin⁡Bb=sin⁡Cc

Given b=2,\ a=3, and B=40 (degrees), determine whether this information

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