To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
We know the base area of the pyramid is \(16 , \text{in}^2\). Let's denote the height of the pyramid as \(h\).
Now, we can set up the equation for the volume of the pyramid:
\[ V = \frac{1}{3} \times 16 \times h \]
We don't have the volume of the pyramid directly, but we do know that the congruent rectangular prism has a volume of \(288 , \text{in}^3\). Since the rectangular prism has the same base area as the pyramid, the volume of the prism can be calculated with the formula:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height}_{\text{prism}} \]
The base area is \(16 , \text{in}^2\), so:
\[ 288 = 16 \times \text{Height}_{\text{prism}} \]
Solving for the height of the prism:
\[ \text{Height}_{\text{prism}} = \frac{288}{16} = 18 , \text{in} \]
Since the volumes of the rectangular prism and pyramid are related in that they have the same base and we know the height of the prism, we equate the volume of the pyramid directly:
\[ \text{Volume of pyramid} = \frac{1}{3} \times 16 \times h = \frac{1}{3} \times 16 \times 18 \]
Setting the volume equal to the prism's volume:
\[ \frac{1}{3} \times 16 \times h = 288 \]
Now we solve for \(h\):
\[ 16h = 288 \times 3 \] \[ 16h = 864 \] \[ h = \frac{864}{16} = 54 , \text{in} \]
Thus, the height of the rectangular pyramid is:
\[ \boxed{54 \text{ in.}} \]