Ambiguous Case Given angle B=14, c=14.0 and b=14.1 How many triangles can be expected. Note that you have to differentiate between right and non-right triangles Select one: a. No triangles b. 1 right triangle c. 1 non-right triangle d. 2 possible triangleSK

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Ambiguous Case   Given angle B=14, c=14.0 and b=14.1   How many triangles can be expected.   Note that you have to differentiate between right and non-right triangles  Select one:   a. No triangles   b. 1 right triangle   c. 1 non-right triangle   d. 2 possible triangleSK

Louise Eldridge · Accepted Answer

Step 1  Sine rule:    sin⁡Bb=sin⁡Cc  ⇒sin⁡(14∘)14⋅1=sin⁡c14  ⇒sin⁡c=14⋅sin⁡(14∘)14⋅1  ⇒sin⁡c=0⋅240206137  C1=23⋅899≈13⋅9∘  C2=180−13⋅9∘≈166⋅1 (Which is Not possible)  ∴B=14, C=23⋅9∘, A=180−(14+13⋅9)  A=152⋅1∘  Step 2  sin⁡Bb=sin⁡Aa  ⇒sin⁡1414⋅1=sin⁡(152⋅2)a⇒a=sin⁡(152⋅1)⋅14⋅7sin⁡14  a=27⋅27 unit  Only one Triangle (Non-Right Triangle) is possible

Ambiguous Case Given angle B = 14,\ c = 14.0 and b = 14.1

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