# Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #48 #, how long are the other two sides?

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Given that two opposite sides of the parallelogram have a length of 12, and the area of the parallelogram is 48, we can use the formula for the area of a parallelogram:

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

Since the height corresponds to the length of the other two sides, we can let (h) represent the length of these sides.

Using the given angle of ( \frac{5\pi}{6} ), we can find the height using the formula:

[ \text{Area} = \text{base} \times \text{height} = 12 \times h \sin(\frac{5\pi}{6}) ]

Solving for (h):

[ h = \frac{\text{Area}}{12 \sin(\frac{5\pi}{6})} ]

[ h = \frac{48}{12 \sin(\frac{5\pi}{6})} ]

[ h = \frac{48}{12 \times \frac{1}{2}} ]

[ h = \frac{48}{6} = 8 ]

So, the length of the other two sides of the parallelogram is 8.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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