1. **State the problem:** Calculate the tangent of the indicated angle $A$ in the right triangle where the vertical leg (opposite to angle $A$) is $4\sqrt{3}$ ft and the horizontal leg (adjacent to angle $A$) is 12 ft. 2. **Formula:** The tangent of an angle in a right triangle is given by $$\tan(A) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Substitute the given values:** $$\tan(A) = \frac{4\sqrt{3}}{12}$$ 4. **Simplify the fraction:** $$\tan(A) = \frac{\cancel{4}\sqrt{3}}{\cancel{12}} = \frac{\sqrt{3}}{3}$$ 5. **Final answer:** $$\boxed{\tan(A) = \frac{\sqrt{3}}{3}}$$ This is the tangent of angle $A$ in lowest terms.