To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the base area of the pyramid is \(16 , \text{in}^2\), let's denote the height of the pyramid as \(h\). Thus, we can express the volume of the pyramid as:
\[ V = \frac{1}{3} \times 16 \times h \]
We also know the volume of the congruent rectangular prism is \(288 , \text{in}^3\). For prisms, the volume formula is:
\[ V = \text{Base Area} \times \text{Height} \]
Using the base area for the prism (which is the same as that of the pyramid, \(16 , \text{in}^2\)), we can write the volume for the prism as:
\[ 288 = 16 \times h_{\text{prism}} \]
To find the height of the prism, we rearrange the equation:
\[ h_{\text{prism}} = \frac{288}{16} = 18 , \text{in} \]
Now, we can find the height of the pyramid using the volume formula. Set the volume equal to \(288\):
\[ 288 = \frac{1}{3} \times 16 \times h \]
Multiplying both sides by 3 gives:
\[ 864 = 16 \times h \]
Now divide both sides by 16:
\[ h = \frac{864}{16} = 54 , \text{in} \]
Thus, the height of the rectangular pyramid is:
\[ \boxed{54 , \text{in.}} \]