To find the exact value of $\tan A$ in simplest radical form for the given right triangle, we use the definition of the tangent function. In a right triangle, $\tan \theta$ is given by the ratio of the opposite side to the adjacent side.

From the diagram:

• The length of side $BC$ (opposite to angle $A$) is 4.
• The length of side $AC$ (adjacent to angle $A$) is 3.

Thus, we have:

$\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AC} = \frac{4}{3}$

So, the exact value of $\tan A$ is $\frac{4}{3}$.

Would you like further explanation or clarification on any part?

Here are some related questions:

1. What is the relationship between the sides of a right triangle and the trigonometric functions?
2. How do you calculate the value of sine and cosine in a right triangle?
3. How do you use the Pythagorean Theorem to find the third side of a right triangle?
4. What is the significance of the 3-4-5 triangle in geometry?
5. How can you use trigonometric functions to solve for unknown angles in a right triangle?

Tip: Remember that the tangent function gives you the ratio of the opposite side to the adjacent side, which is useful for finding angles and solving trigonometric problems in right triangles.