# Two opposite sides of a parallelogram each have a length of #5 #. If one corner of the parallelogram has an angle of #(5 pi)/8 # and the parallelogram's area is #15 #, how long are the other two sides?

The other two side are long

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Given the length of the opposite sides of the parallelogram is 5 and one angle is ( \frac{5\pi}{8} ), we can use the formula for the area of a parallelogram:

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

Given the area is 15 and the base is 5, we can solve for the height:

[ 15 = 5 \times \text{height} ] [ \text{height} = \frac{15}{5} = 3 ]

Now, we can find the length of the other two sides using trigonometry. Since one of the angles is ( \frac{5\pi}{8} ), the other angle in the parallelogram is also ( \frac{5\pi}{8} ).

Using sine and cosine, we can find the lengths of the other two sides:

[ \text{Adjacent side} = \text{Adjacent side} = 5 \cos\left(\frac{5\pi}{8}\right) ] [ \text{Opposite side} = \text{Opposite side} = 5 \sin\left(\frac{5\pi}{8}\right) ]

Calculating these values:

[ \text{Adjacent side} \approx 5 \times 0.3827 \approx 1.9135 ] [ \text{Opposite side} \approx 5 \times 0.9239 \approx 4.6195 ]

So, the lengths of the other two sides are approximately 1.9135 and 4.6195.

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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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