1. The problem is to solve for $a$ in the equation $\tan 9^\circ = \frac{a}{2.1}$. We want to find the value of $a$ to 2 decimal places. 2. The formula used here is the definition of tangent in a right triangle or ratio form: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 9^\circ$, opposite side is $a$, and adjacent side is 2.1. 3. To solve for $a$, multiply both sides of the equation by 2.1: $$\tan 9^\circ = \frac{a}{2.1} \implies a = 2.1 \times \tan 9^\circ$$ 4. Calculate $\tan 9^\circ$ using a calculator: $$\tan 9^\circ \approx 0.1584$$ 5. Substitute this value back: $$a = 2.1 \times 0.1584 = 0.33264$$ 6. Round $a$ to 2 decimal places: $$a \approx 0.33$$ Therefore, the solution is $a = 0.33$.