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

Using the parallelogram pictured, find the length of the shorter diagonal. Round your-example-1

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5 votes

Answer:

21 in

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

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