Tan 30 F9515E

1. The problem is to find the value of $\tan 30^\circ$. 2. Recall the definition of tangent in a right triangle: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$. 3. For special angles like $30^\circ$, we use known exact values from the unit circle or special triangles. 4. The value of $\tan 30^\circ$ is $\frac{1}{\sqrt{3}}$. 5. To rationalize the denominator, multiply numerator and denominator by $\sqrt{3}$: $$\tan 30^\circ = \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$ 6. Therefore, the exact value of $\tan 30^\circ$ is $\frac{\sqrt{3}}{3}$. Final answer: $\boxed{\frac{\sqrt{3}}{3}}$