Answer:
21 in
Step-by-step explanation:
The law of cosines is helpful for this. The angle opposite the shorter diagonal is the supplement of the angle shown, so is 60°.
If we designate the known sides as "a" and "b", the short diagonal as "c" and the smaller angle as C, then the law of cosines tells us ...
c^2 = a^2 + b^2 -2ab·cos(C)
For the given dimensions, we have ...
c = √(15^2 +24^2 -2·15·24·cos(60°)) = √441 = 21 . . . inches
