# Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #36 #, how long are the other two sides?

Length of other two sides

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The area of a parallelogram can be calculated using the formula: ( \text{Area} = \text{base} \times \text{height} ).

Given that the area of the parallelogram is 36 and one of its sides (the base) has a length of 8, we can find the height.

Let's denote the height of the parallelogram as ( h ). Thus, we have:

( 36 = 8 \times h )

Solving for ( h ), we find ( h = 4.5 ).

Now, to find the lengths of the other two sides, we use trigonometry. Given that one angle of the parallelogram is ( \frac{3\pi}{8} ), and knowing that opposite angles in a parallelogram are equal, the other opposite angle will also be ( \frac{3\pi}{8} ).

We can use trigonometric functions to find the lengths of the other two sides. Since we have the adjacent side (8) and the angle (( \frac{3\pi}{8} )), we can use cosine.

Let's denote one of the other sides as ( a ). Therefore, we have:

( \cos\left(\frac{3\pi}{8}\right) = \frac{8}{a} )

Solving for ( a ), we find ( a \approx 10.847 ).

Since opposite sides of a parallelogram are equal in length, the other side also has a length of approximately 10.847 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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