To find the length of the diagonals of a rectangular prism (in this case, the coffee table), we can use the three-dimensional diagonal formula. The formula for the length of the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Given:
- Length \( l = 44 \) in.
- Width \( w = 24 \) in.
- Height \( h = 14 \) in.
Now we substitute the values into the formula:
\[ d = \sqrt{44^2 + 24^2 + 14^2} \]
Calculating each term:
\[ 44^2 = 1936 \] \[ 24^2 = 576 \] \[ 14^2 = 196 \]
Now, add these values:
\[ d = \sqrt{1936 + 576 + 196} \] \[ d = \sqrt{2708} \]
Now calculate \( \sqrt{2708} \):
\[ \sqrt{2708} \approx 52.0 \]
Thus, the length of each diagonal, rounded to the nearest tenth, is:
\[ \boxed{52.0} \text{ in.} \]