Question

determine the length of side cb.

Explanation:

Step1: Identify trigonometric ratio

In right $\triangle ABC$, $\angle B=30^\circ$, $AC=5$ (opposite $\angle B$), $CB$ is adjacent to $\angle B$. Use tangent:
$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(30^\circ)=\frac{5}{CB}$
We know $\tan(30^\circ)=\frac{1}{\sqrt{3}}$, so:
$\frac{1}{\sqrt{3}}=\frac{5}{CB}$

Step3: Solve for $CB$

Rearrange to isolate $CB$:
$CB=5\sqrt{3}$

Answer:

$5\sqrt{3}$