Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?

Answer 1

#=0.26#

Area of the rhombus with angle #theta=(7pi)/12# and Side #a=1# is #=a^2 sin theta# #=1^2 sin((7pi)/12)# #=1(0.966)# #=0.966# Area of the rhombus with angle #theta=pi/4# and Side #a=1# is #=a^2 sin theta# #=1^2 sin((pi)/4)# #=1(0.707)# #=0.707# So difference in Area#=0.966-0.707=0.26#
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Answer 2

To find the areas of the rhombuses, we use the formula:

Area = (1/2) * d1 * d2, where d1 and d2 are the diagonals of the rhombus.

For a rhombus with side length 1, the diagonals can be found using the sine formula for a triangle:

d1 = 2 * sin(angle/2) * side d2 = 2 * sin((π - angle)/2) * side

Substitute the given angles into the formulas and calculate the diagonals for both rhombuses. Then, use the area formula to find the areas of both rhombuses and subtract one from the other to get the difference in their areas.

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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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