Question Type 8: Given the triangle suffers from ambiguous case, finding both possible angles Exercises

In triangle $ABC$, side $a = 7.5$, side $b = 10.2$, and angle $A = 37^\circ$. Determine both possible triangles by finding the two values of angle $B$ and the corresponding angles $C$.

In triangle $ABC$, $a = 7$, $b = 10$, and $A = 25^\circ$. Determine the two possible values of angle $B$.

In triangle $ABC$, side $a = 5$, side $b = 9$, and angle $B = 25^\circ$. Calculate the possible values of angle $A$.

In triangle $ABC$, $\sin A = 0.8$. Find the two possible values of angle $A$. Give your answers correct to 2 decimal places.

In triangle $ABC$, side $a = 11$, side $b = 6$, and $\angle B = 28^\circ$. Find the two possible values of $\angle A$.

In triangle $ABC$, side $a = 12$, side $b = 13$, and $\sin B = 0.6$. Determine the two possible measures of angle $B$.

In triangle $ABC$, side $a = 8.2$, side $b = 11.4$, and $\angle A = 28.5^\circ$. Find both possible triangles by determining angles $B$ and $C$.

In triangle $ABC$, side $a = 9$, side $b = 12$, and $\angle A = 41^\circ$. Determine the two possible measures of $\angle B$.

In triangle ABC, side $a = 7$, side $b = 9$, and $\angle A = 40^\circ$. Calculate the two possible values of $\angle B$.

In triangle $ABC$, side $a = 9.6$, side $b = 7.2$, and $\angle B = 35.4^\circ$. Compute both possible values of $\angle A$ and the corresponding side $c$.

In triangle $ABC$, side $a = 8$, side $b = 15$, and $\angle A = 32^\circ$. Find the two possible values of $\angle B$.

Find both possible values of $\angle B$ and then calculate the corresponding side $c$ in each case.