To find the height of a right rectangular prism, we can use the formula for the volume of a rectangular prism:
\[ V = \text{length} \times \text{width} \times \text{height} \]
We are given:
- Volume \( V = 75 , \text{cm}^3 \)
- Length \( \text{length} = 2 , \text{cm} \)
- Width \( \text{width} = 10 , \text{cm} \)
We need to find the height \( h \).
Rearranging the formula to solve for height, we get:
\[ h = \frac{V}{\text{length} \times \text{width}} \]
Substituting the values we have:
\[ h = \frac{75}{2 \times 10} \]
Calculating the denominator:
\[ 2 \times 10 = 20 \]
Now substituting it back into the equation for height:
\[ h = \frac{75}{20} = 3.75 , \text{cm} \]
Thus, the height of the right rectangular prism is \( \boxed{3.75} , \text{cm} \).