Using the parallelogram pictured, find the length of the shorter diagonal. round your answer to the nearest inch.

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

linear pair postulates