Question

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Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides for $\angle A = 30^\circ$

Opposite side to $30^\circ$ is $5$ cm (side $BC$), adjacent side is $b$ (side $AC$).

Step3: Apply tangent formula

So $\tan(30^\circ) = \frac{5}{b}$.

Answer:

$\tan(30^\circ) = \frac{5}{b}$ (the first option)