A

Step 1: To find the angle \( \theta \) that the vector A makes with the X-axis, we can use the tangent function, which relates the angle to the opposite and adjacent sides in a right triangle.

Step 2: The components of vector A are given as:
\( A_x = 4 \, \text{units} \) (adjacent side)
\( A_y = 3 \, \text{units} \) (opposite side)

Step 3: The angle \( \theta \) can be calculated using:
\( \tan(\theta) = \frac{A_y}{A_x} = \frac{3}{4} \)

Step 4: To find \( \theta \), we take the inverse tangent (also called arctan):
\( \theta = \tan^{-1}\left(\frac{3}{4}\right) \)

Step 5: Using a calculator, we find: \( \theta \approx 36.87^{\circ} \).

Therefore, the angle which the vector makes with the X-axis is approximately 36.87 degrees.