IB Mathematics Applications & Interpretation 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 $b=19$.