Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/6 #, what is the difference between the areas of the rhombuses?

Answer 1

#=4.19#

Area of rhombus with angle #theta=a^2 sintheta# where #a# is the side. So Area #A1#of rhombus with side-length #3# and angle #7pi/12# can be written as #A1=(3^2) sin(7pi/12)# or #A1=9sin(7pi/12)# or #A1=8.69# And Area #A2#of rhombus with side-length #3# and angle #pi/6# can be written as #A2=(3^2) sin(pi/6)# or #A2=9 sin(pi/6)# or #A2=4.5# The difference #=A2-A1# #=8.69-4.5# #=4.19#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2. For a rhombus with side length ( s ) and acute angle ( \theta ), the diagonals have lengths ( d_1 = s/\sin(\theta) ) and ( d_2 = s/\sin(\pi/2 - \theta) ).

Using this information, the area of the rhombus with angle ( \frac{7\pi}{12} ) is ( A_1 = \frac{(3/\sin(7\pi/12))^2}{2} ). The area of the rhombus with angle ( \frac{\pi}{6} ) is ( A_2 = \frac{(3/\sin(\pi/6))^2}{2} ).

Calculate both areas and find the difference: ( A_1 - A_2 ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7