Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #132 #, how long are the other two sides?
The two other sides are 10.0816 long each
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Using the given information, the lengths of the other two sides of the parallelogram can be calculated using the formula for the area of a parallelogram, (A = bh), where (b) is the base and (h) is the height. The height of the parallelogram can be found by using the formula (h = b \cdot \sin(\theta)), where (\theta) is the given angle. Substituting the known values into these formulas:
Given:
 Length of one side ((b)): 12
 Angle ((\theta)): (\frac{5\pi}{12})
 Area ((A)): 132
Calculations:

Calculate the height ((h)): [h = 12 \cdot \sin\left(\frac{5\pi}{12}\right)]

Calculate the value of (h).

Use the formula for the area to find the length of the other side ((b_2)): [b_2 = \frac{A}{h}]

The length of the opposite side is the same as (b_2), as opposite sides of a parallelogram are equal in length.
Perform the calculations to find the lengths of the other two sides of the parallelogram.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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