Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

Answer 1
We know the area (A )of a rhombus is #A=a^2sintheta#,where a is the length of the side and #theta # is the angle between two sides, For 1st Rhombus #theta =pi/12,a=3# So Area #A_1=3^2sin(pi/12)=2.33squnit#
For 2nd Rhombus #theta =7pi/8,a=3# So Area #A_2=3^2sin(7xxpi/12)=8.69squnit#
So difference between the area #Delta A=A_2_A_1=8.69-2.33=6.36squnit#
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Answer 2

The difference between the areas of the two rhombuses can be calculated using their diagonal lengths. Since the sides of both rhombuses have lengths of 3, their diagonals can be calculated using trigonometric properties.

For a rhombus with an angle of ( \frac{\pi}{12} ), the diagonal lengths are ( 3\sqrt{2} ) and ( 3\sqrt{6} ), and for a rhombus with an angle of ( \frac{7\pi}{8} ), the diagonal lengths are ( 3\sqrt{2} ) and ( 3\sqrt{6} ).

The difference between the areas of the rhombuses is zero since they have identical diagonal lengths.

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Answer from HIX Tutor

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.

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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