To find the height of the rectangular prism, we can use the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
First, we rearrange the formula to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
We know the mass is 1,260 grams and the density is 1.2 g/cm³:
\[ \text{Volume} = \frac{1260 , \text{g}}{1.2 , \text{g/cm}^3} = 1050 , \text{cm}^3 \]
Next, we can find the volume of the rectangular prism using the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
We know the length (8 cm) and the width (15 cm), so we can express the volume as:
\[ 1050 , \text{cm}^3 = 8 , \text{cm} \times 15 , \text{cm} \times \text{Height} \]
Now, calculating the area of the base:
\[ 8 \times 15 = 120 , \text{cm}^2 \]
Now we can find the height \( h \):
\[ 1050 = 120 \times h \]
Solving for \( h \):
\[ h = \frac{1050}{120} = 8.75 , \text{cm} \]
Thus, the height of the prism is:
\[ \boxed{8.75} \] cm.