# Two opposite sides of a parallelogram each have a length of #10 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #80 #, how long are the other two sides?

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Let the length of one of the other sides of the parallelogram be (a) and the length of the corresponding adjacent side be (b).

Given that the area of the parallelogram is 80, we can use the formula for the area of a parallelogram: ( \text{Area} = \text{base} \times \text{height} ).

Since one of the sides is given as 10 and the angle opposite to it is ( \frac{\pi}{3} ), the height of the parallelogram can be found using the formula: ( \text{height} = 10 \times \sin\left(\frac{\pi}{3}\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} ).

Now, we can set up the equation to find the other side:

( \text{Area} = 80 = a \times 5\sqrt{3} ).

Solve for (a):

( a = \frac{80}{5\sqrt{3}} = \frac{16\sqrt{3}}{3} ).

Thus, one of the other sides of the parallelogram is ( \frac{16\sqrt{3}}{3} ).

Since opposite sides of a parallelogram are equal in length, the length of the other side is also ( \frac{16\sqrt{3}}{3} ).

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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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