In right triangle \( ABC \), we have the following information: the height \( CD \) is given as \( 3 \) and \( DB \) is given as \( 4 \). We want to find the length of \( AD \).
From the problem setup, we'll assume:
- \( D \) is the foot of the altitude \( CD \) from vertex \( C \) to hypotenuse \( AB \).
- \( AD \) and \( DB \) are segments of the hypotenuse \( AB \).
According to the properties of similar triangles, when an altitude is drawn to the hypotenuse of a right triangle, it creates two smaller right triangles that are similar to each other and to the original triangle.
Let:
- \( AD = x \)
- \( DB = 4 \)
According to the property of the altitude in a right triangle:
\[ CD^2 = AD \times DB \] \[ 3^2 = x \times 4 \] \[ 9 = 4x \] \[ x = \frac{9}{4} \] \[ x = 2.25 \]
Thus, the length of \( AD \) is:
\[ AD = 2.25 \]
Rounded to two decimal places, the length of \( AD \) is:
\[ \boxed{2.25} \]