Given b=2,a=3, and B=40 (degrees), determine whether this information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangles.

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SabadisO · Accepted Answer

Step 1 Given that, 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∘ =65.4∘ 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 informati

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