To find the height of a right rectangular prism, we can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
We are given:
- Volume = 75 cm³
- Length = 2 cm
- Width = 10 cm
We need to find the height. We can rearrange the formula to solve for height:
\[ \text{height} = \frac{\text{Volume}}{\text{length} \times \text{width}} \]
Substituting in the values:
\[ \text{height} = \frac{75 , \text{cm}^3}{2 , \text{cm} \times 10 , \text{cm}} \]
Calculating the denominator:
\[ 2 , \text{cm} \times 10 , \text{cm} = 20 , \text{cm}^2 \]
Now substituting this into the height formula:
\[ \text{height} = \frac{75 , \text{cm}^3}{20 , \text{cm}^2} \]
Calculating the height:
\[ \text{height} = 3.75 , \text{cm} \]
Thus, the height of the right rectangular prism, rounded to the nearest hundredth, is:
\[ \boxed{3.75} \text{ cm} \]