In triangle $XYZ$, angle $X$ measures 20 degrees, the side opposite it measures $13$, and the side opposite angle $Y$ measures $15$. Which pair gives the two possible measures of angle $Y$?

In triangle $XYZ$, angle $X$ measures 29 degrees, the side opposite it measures $6$, and the side opposite angle $Y$ measures $20$. How many triangles fit these measurements?

In triangle $DEF$, angle $D$ measures 28 degrees, the side opposite it measures $10$, and the side opposite angle $E$ measures $15$. How many triangles fit these measurements?

In triangle $JKL$, angle $J$ measures 31 degrees, the side opposite it measures $17$, and the side opposite angle $K$ measures $18$. Which pair gives the two possible measures of angle $K$?

In triangle $DEF$, angle $D$ measures 27 degrees, the side opposite it measures $16$, and the side opposite angle $E$ measures $24$. The height from $F$ to line $DE$ is $h=b\sin D$. Which statement gives $h$ and the conclusion it forces?

In triangle $RST$, angle $R$ measures 53 degrees, the side opposite it measures $4$, and the side opposite angle $S$ measures $10$. Which statement explains why no triangle has these measurements?

In triangle $ABC$, angle $A$ measures 64 degrees, the side opposite it measures $16$, and the side opposite angle $B$ measures $20$. The height from $C$ to line $AB$ is $h=b\sin A$. Which statement gives $h$ and the conclusion it forces?

In triangle $RST$, angle $R$ measures 22 degrees, the side opposite it measures $8$, and the side opposite angle $S$ measures $20$. How many triangles fit these measurements?

In triangle $UVW$, angle $U$ measures 125 degrees, the side opposite it measures $10$, and the side opposite angle $V$ measures $14$. How many triangles fit these measurements?

In triangle $UVW$, angle $U$ measures 27 degrees, the side opposite it measures $11$, and the side opposite angle $V$ measures $18$. Taking the solution in which angle $V$ is obtuse and measures about 132.0 degrees, which value is closest to the side opposite angle $W$?

In triangle $RST$, angle $R$ measures 30 degrees, the side opposite it measures $9$, and the side opposite angle $S$ measures $15$. Which pair gives the two possible measures of angle $S$?

In triangle $KLM$, angle $K$ measures 43 degrees, the side opposite it measures $8$, and the side opposite angle $L$ measures $14$. Which statement explains why no triangle has these measurements?

In triangle $ABC$, angle $A$ measures 56 degrees, the side opposite it measures $12$, and the side opposite angle $B$ measures $20$. The height from $C$ to line $AB$ is $h=b\sin A$. Which statement gives $h$ and the conclusion it forces?

In triangle $KLM$, angle $K$ measures 140 degrees, the side opposite it measures $9$, and the side opposite angle $L$ measures $25$. How many triangles fit these measurements?

In triangle $JKL$, angle $J$ measures 69 degrees, the side opposite it measures $13$, and the side opposite angle $K$ measures $20$. The height from $L$ to line $JK$ is $h=b\sin J$. Which statement gives $h$ and the conclusion it forces?

In triangle $ABC$, angle $A$ measures 49 degrees, the side opposite it measures $11$, and the side opposite angle $B$ measures $12$. Which pair gives the two possible measures of angle $B$?

In triangle $KLM$, angle $K$ measures 50 degrees, the side opposite it measures $16$, and the side opposite angle $L$ measures $20$. Taking the solution in which angle $L$ is obtuse and measures about 106.8 degrees, which value is closest to the side opposite angle $M$?

In triangle $JKL$, angle $J$ measures 27 degrees, the side opposite it measures $10$, and the side opposite angle $K$ measures $16$. Taking the solution in which angle $K$ is obtuse and measures about 133.4 degrees, which value is closest to the side opposite angle $L$?

In triangle $ABC$, angle $A$ measures 58 degrees, the side opposite it measures $15$, and the side opposite angle $B$ measures $15$. The height from $C$ to line $AB$ is $h=b\sin A$. What is $h$, and how many triangles fit?

In triangle $RST$, angle $R$ measures 68 degrees, the side opposite it measures $12$, and the side opposite angle $S$ measures $18$. The height from $T$ to line $RS$ is $h=b\sin R$. Which statement gives $h$ and the conclusion it forces?