Triangles

$ABC$ is a triangle with the sides of lengths $c=15$, $b=6$, and the measure of $\measuredangle CAB$ is ${150}^{\circ }$. Which of the numbers gives the size of the angle $BCA$ most accurately?

In an isosceles triangle $ABC$, the base $AB=6\mathrm{cm}$, the measure of the angle $ABC$ is ${20}^{\circ }$. The angle bisector of the angle $BAC$ intersects the side $BC$ at a point $K$. Find the length of the line segment $BK$. Round the result to two decimal places.

In a triangle $ABC$, $c=2\mathrm{cm}$, $a=3\mathrm{cm}$ and $\beta ={60}^{\circ }$. What is the length of side $b$?

Given a triangle $ABC$, the length of the median from $C$ is $9\mathrm{cm}$ and the length of the median from $B$ is $6\mathrm{cm}$. Let $T$ be the centroid, and $S$ be the midpoint of $AC$. The measure of the angle $BTC$ is ${120}^{\circ }$. Find the length of the side $AC$.