# Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #28 #, how long are the other two sides?

Opposite angles are equal so A=C

The sum of all the angles is

So Angle D is:

#Area of a parallelogram is:

So other two sides are:

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Given that the opposite sides of the parallelogram each have a length of 4, and one of the angles is ( \frac{2\pi}{3} ), we can use trigonometry to find the lengths of the other two sides.

The area of a parallelogram is given by the formula:

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

We can find the height of the parallelogram using the formula for the area and the given length of one of the sides (4).

[ \text{Area} = 28 ] [ \text{base} = 4 ] [ \text{height} = \frac{\text{Area}}{\text{base}} = \frac{28}{4} = 7 ]

Now, we can use trigonometry to find the lengths of the other two sides. In a parallelogram, opposite sides are equal in length.

Given that one angle is ( \frac{2\pi}{3} ), the adjacent side (the side sharing the angle) can be found using trigonometric functions.

[ \text{adjacent side} = \text{base} \times \cos(\text{angle}) ] [ \text{adjacent side} = 4 \times \cos\left(\frac{2\pi}{3}\right) ]

Using the values, we find:

[ \text{adjacent side} = 4 \times \cos\left(\frac{2\pi}{3}\right) = 4 \times \left(-\frac{1}{2}\right) = -2 ]

The negative sign indicates that we're going in the opposite direction.

Since opposite sides of a parallelogram are equal in length, the other side opposite to the given side will also be 4 units.

So, the lengths of the other two sides are both 4 units.

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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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