Question Type 7: Determining if the triangles suffer from ambiguous case of sine rule Exercises

Given $A=30^\circ$, $a=10$, and $b=5$, determine the number of possible triangles and their angles.

Given that $A$ is an acute angle such that $\sin A = 0.8$, $a = 10$, and $b = 5$, determine the number of possible triangles and find all valid angles $A$, $B$, and $C$.

In triangle $ABC$, $\sin A = 0.6$ where $A$ is acute, $a = 9$, and $b = 7$. Determine the number of possible triangles and find the measures of angles $B$ and $C$.

Given $A=40^\circ$, $a=12$, and $b=9$, determine whether two triangles are possible and list all angles.

Given $A=70^\circ$, $a=8$, and $b=5$, find the unknown angles of all valid triangles.

Given $\sin A = 0.8$ where $A$ is acute, $a = 10$, and $b = 7$, determine how many triangles satisfy the conditions and find all sets of angles.

Given $A=45^\circ$, $a=14$, and $b=10$, assess the ambiguous case and find all valid angles.

Given $A=50^\circ$, $a=10$, and $b=6$, decide if the ambiguous case applies and find all possible triangles.

Given $A=60^\circ$, $a=12$, and $b=6$, determine if two triangles can be formed and list their angles.

Given an acute angle $A$ such that $\sin A = 0.5$, $a = 8$, and $b = 5$, determine whether the ambiguous case arises and find the unknown angles of all valid triangles.

Given $\sin A = 0.9$ where $A$ is acute, $a = 15$, and $b = 12$, determine the number of solutions and find all valid angles.