$\,$A set of information that will give $2$ sets of solutions is considered ambiguous. $\,$Amb

Question

$\,$A set of information that will give $2$ sets of solutions is considered ambiguous. $\,$Ambiguous cases when solving a triangle arise because sine ratio of an ACUTE or OBTUSE angle are both positive. Let $a$ and $b$ be opposite $A$ and $B$. For acute $A$, exactly two triangles occur when $b\sin A<a<b$. The condition $a<b$ alone is insufficient: check the sine range, both supplementary candidates for $B$, and $A+B<180^\circ$. Draw the possible triangles $ABC$, where $a=\sqrt{29}\approx5.39$ units, $b=\sqrt{50}\approx7.07$ units and angle $BAC=45{}^\circ $ .

Accepted Answer

$(B,C,c)=(68.2^\circ,66.8^\circ,7\text{ units})$ or $(111.8^\circ,23.2^\circ,3\text{ units})$

Ambiguous Cases of Sine Rule

Ambiguous Cases of Sine Rule

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