# Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #18 #, how long are the other two sides?

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First, find the length of the diagonal using the area of the parallelogram formula: ( \text{Area} = \text{base} \times \text{height} \times \sin(\theta) ), where ( \theta ) is the angle between the given sides.

Given:

- Length of one side = 4
- Area of parallelogram = 18
- Angle ( \theta = \frac{7\pi}{8} )

Substitute these values into the area formula to get: ( 18 = 4 \times \text{height} \times \sin\left(\frac{7\pi}{8}\right) )

Solve for the height: ( \text{height} = \frac{18}{4 \times \sin\left(\frac{7\pi}{8}\right)} )

Once you have the height, you can use the Pythagorean theorem to find the lengths of the other two sides since the diagonals of a parallelogram bisect each other. This can be expressed as ( \text{Diagonal}^2 = \text{base}^2 + \text{height}^2 ).

Calculate the height and then use it to find the lengths of the other two sides using the Pythagorean theorem.

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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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- Find the equation of a line passing through #(1,1/2)# and making an angle #pi/6# to the line #y=1/2x#?

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