Triangle trigonometry and its applications practice questions — IB Maths AA

In $\mathrm{△}ABC$, $a=6$ and $\mathrm{\angle }A={\displaystyle \frac{\pi }{6}}$. The circumradius $R$ equals:

In $\mathrm{△}ABC$, $\mathrm{\angle }A={\displaystyle \frac{\pi }{6}}$, $\mathrm{\angle }B={\displaystyle \frac{\pi }{4}}$, and $a=4$. The side $b$ equals:

The area of a triangle with sides $5$, $6$, $7$ is closest to:

In a triangle, $a$ is opposite $\mathrm{\angle }A={30}^{\circ }$ and $b$ is opposite $\mathrm{\angle }B={90}^{\circ }$. If $a=5$, then $b$ equals:

In $\mathrm{△}ABC$, $AB=5$, $BC=12$, $AC=13$. The area equals:

In a triangle, two sides have lengths $4$ and $5$ and the included angle is ${60}^{\circ }$. The length of the third side is:

In $\mathrm{△}ABC$, $a=5$, $b=6$, $c=7$. The inradius $r$ is closest to:

A right triangle has legs $3$ and $4$. Its area equals:

In $\mathrm{△}ABC$, $AB=6$, $AC=8$, and $\mathrm{\angle }A={\displaystyle \frac{\pi }{6}}$. The area equals:

In $\mathrm{△}ABC$, $a=7$, $b=8$, $c=5$. The value of $\cos C$ is: