# Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #(5 pi)/8 # and the parallelogram's area is #64 #, how long are the other two sides?

The other two sides are

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To find the lengths of the other two sides of the parallelogram, given that two opposite sides have a length of 16 and the area is 64, and one angle is ( \frac{5\pi}{8} ), you can use the formula for the area of a parallelogram:

[ \text{Area} = \text{base} \times \text{height} ]

In this case, since two opposite sides form a base, and the height is the perpendicular distance between these sides, you can find the height using trigonometry:

[ \text{Height} = 16 \times \sin\left(\frac{5\pi}{8}\right) ]

Once you find the height, you can use it to calculate the lengths of the other two sides. Since the opposite sides of a parallelogram are equal in length:

[ \text{Other side length} = \sqrt{16^2 - (\text{Height})^2} ]

Calculate the height using the given angle and then find the lengths of the other two sides using the formula above.

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