Question Type 4: Determining if given information on a triangle suffers from Ambigious case of sine rule Exercises

Determine whether a triangle is possible for $\sin A = 0.6$, $a = 8$, and $b = 3$. Provide a justification.

Determine whether a triangle exists given $\sin A = 0.8$, $a = 10$, and $b = 5$. Explain your reasoning.

Determine whether the given data $\sin A = 0.8$, $a = 10$, and $b = 9$ yields one triangle, two triangles, or no triangle. Justify your answer.

Check if a triangle exists for $\sin A = 0.9$, $a = 20$, and $b = 15$, and justify your answer.

Given $\sin A = 0.5$, $a = 12$, and $b = 7$, find all possible values of angle $B$.

For $\sin A = 0.6$, $a = 8$, and $b = 7$, determine all possible measures of angle $B$.

Given $\sin A = 0.7$, $a = 15$, and $b = 12$, find both possible angles $B$.

For $\sin A = 0.4$, $a = 25$, and $b = 18$, find both possible values of angle $B$.

For the data $\sin A = 0.5$, $a = 12$, and $b = 7$, calculate the corresponding measures of angle $C$ for both possible triangles.

Determine all possible values of $B$ if $\sin A = 0.9$, $a = 20$, and $b = 19$.

Using $\sin A = 0.7$, $a = 15$, and $b = 12$, calculate side $c$ for each possible triangle.