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Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?

Answer 1

Sadie Allen

Difference between the areas of two rhombuses is #0.74(2dp) sq.unit#

Sides and corner angle of rhombus #1# are #s_1=1 , theta_1=pi/12=15^0#

Area of rhombus #1# is #A_1 =s_1^2*sin theta_1= 1*sin15 ~~0.2588 sq.unit#

Sides and corner angle of rhombus #2# are #s_2=1 , theta_2=pi/2=90^0#

Area of rhombus #2# is #A_2 =s_2^2*sin theta_2= 1*sin90 =1 sq.unit#

Difference between the areas of two rhombuses is #1-0.2588~~0.74(2dp) sq.unit# [Ans]

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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.