Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?

Answer 1

Noah Atkinson

Diff. between areas of the rhombuses = 11.21#

Area of Rhombus #A_r = a^2 sin theta#

#a= 5, theta_1 = pi/12, theta_2 = (3pi)/4#

#A_(r1) = 5^2 * sin (pi/12) = 6.47#

#A_(r2) = 5^2 * sin ((3pi)/4) = 17.68#

Diff. between the rhombuses = 17.68 - 6.47 = 11.21#

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Answer 2

Mason Adams

The difference between the areas of the two rhombuses is ( 5(5 \cos(\pi/12))^2 - 5(5 \cos(3\pi/4))^2 ), which simplifies to ( 5(5 \cos(\pi/12))^2 - 5(5 \sin(\pi/4))^2 ). After calculations, the difference is approximately ( 10.153 ).

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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.