# Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #(7pi)/8 # and the other has a corner with an angle of #(pi)/6 #, what is the difference between the areas of the rhombuses?

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The difference between the areas of the two rhombuses can be calculated using the formula for the area of a rhombus, which is given by ( A = \frac{1}{2} \times d_1 \times d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals. Since the sides of both rhombuses are 3 units long, the length of each diagonal can be found using trigonometry.

For the rhombus with an angle of ( \frac{7\pi}{8} ) at one corner, the diagonals can be found as follows:

[ d_1 = 2 \times 3 \times \sin\left(\frac{7\pi}{16}\right) ] [ d_2 = 2 \times 3 \times \sin\left(\frac{9\pi}{16}\right) ]

Similarly, for the rhombus with an angle of ( \frac{\pi}{6} ) at one corner:

[ d_1' = 2 \times 3 \times \sin\left(\frac{\pi}{3}\right) ] [ d_2' = 2 \times 3 \times \sin\left(\frac{\pi}{6}\right) ]

Calculate the values of ( d_1 ), ( d_2 ), ( d_1' ), and ( d_2' ), then substitute these values into the area formula for each rhombus:

[ A_1 = \frac{1}{2} \times d_1 \times d_2 ] [ A_2 = \frac{1}{2} \times d_1' \times d_2' ]

Finally, find the difference between the areas ( A_1 ) and ( A_2 ) to get the answer.

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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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