To find the height of the right rectangular prism, we can use the formula for the volume of a prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
We have the length (L) = 2 cm, the width (W) = 10 cm, and the volume (V) = 75 cm³. We need to solve for the height (H).
Substituting the known values into the formula:
\[ 75 = 2 \times 10 \times H \]
Calculating the product of length and width:
\[ 75 = 20 \times H \]
Next, we solve for H by dividing both sides by 20:
\[ H = \frac{75}{20} \]
Calculating the division:
\[ H = 3.75 \]
Thus, the height of the prism is \( \boxed{3.75} \) cm.