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

Determine whether a triangle $ABC$ exists for $\sin A = 0.9$, $a = 15$, and $b = 20$. Justify your answer.

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

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

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

In triangle $ABC$, $\sin A = 0.4$, $a = 12$, and $b = 18$.

Find both possible values of angle $B$. Give your answers correct to one decimal place.

Determine whether a triangle $ABC$ is possible given $\sin A = 0.6$, $a = 3$, and $b = 8$. Justify your answer.

Given $\sin A = 0.7$, $a = 15$, and $b = 12$, find the possible value(s) 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 $b = 19$.