IB Mathematics Applications & Interpretation Question Type 5: Finding Both Possible Triangles for Those Suffering with Ambigious Case of Sine Rule Exercises

In triangle ABC, $a=15$, $b=17$ and $A=45^{\circ }$. Determine both possible triangles (angles $B$, $C$, side $c$).

In triangle ABC, $a=14$, $b=20$ and $A=25^{\circ }$. Find both possible values of $B$, $C$ and $c$.

In triangle $ABC$, $a=5$, $b=6$ and $\sin A=0.8$. Determine both possible sets of values for angle $B$, angle $C$, and the side $c$.

In triangle ABC, $a=8$, $b=9$ and $A=30^{\circ }$. Find both possible sets of angles $B$, $C$ and side $c$.

In triangle $ABC$, $a=7$, $b=9$ and $A=40^{\circ }$. Find both possible values of $B$, $C$ and $c$.

In triangle $ABC$, $a=11$, $b=13$ and $\hat{A}=35^{\circ }$. Determine both possible triangles, finding the values for angles $B$ and $C$, and side length $c$.

In triangle $ABC$, $a=6$, $b=8$ and $A=25^{\circ }$. Determine both possible triangles by finding the missing angles $B$ and $C$, and the side length $c$.

In triangle $ABC$, $a=9$, $b=14$ and $A=20^{\circ }$. Find both possible values of $B$, $C$, and $c$.

In triangle $ABC$, $a=12$, $b=14$ and $A=50^{\circ }$. Determine both possible triangles, stating the values for angle $B$, angle $C$, and side $c$.

In triangle $ABC$, $a=10$, $b=11$, and $\hat{A}=50^{\circ }$. Find both sets of possible values for $\hat{B}$, $\hat{C}$, and side $c$.

In triangle $ABC$, $a=9$, $b=10$, and $A=60^{\circ }$. Find both sets of possible values for angle $B$, angle $C$, and side $c$.

In triangle $ABC$, $a=6$, $b=6.2$ and $A=70^{\circ }$. Determine both possible triangles by finding the angles $B$, $C$ and the side $c$ for each case.