# Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #24 #, how long are the other two sides?

Other two sides are

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

Let ( a ) and ( b ) be the lengths of the other two sides of the parallelogram.

Given that the area of the parallelogram is ( 24 ) and one side has a length of ( 12 ), the area can also be expressed as the product of the base and the height. Since the height is the length of the side perpendicular to the given side, it can be calculated as ( b \sin\left(\frac{3\pi}{8}\right) ).

So, we have:

[ 24 = 12 \cdot b \cdot \sin\left(\frac{3\pi}{8}\right) ]

Now, solve for ( b ):

[ b = \frac{24}{12 \cdot \sin\left(\frac{3\pi}{8}\right)} ]

[ b = \frac{24}{12 \cdot \sin\left(\frac{3\pi}{8}\right)} ]

[ b = \frac{2}{\sin\left(\frac{3\pi}{8}\right)} ]

Now, we can use the fact that opposite sides of a parallelogram are equal in length, so ( a = 12 ) as well.

Thus, the lengths of the other two sides are both ( 12 ) units.

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

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.

- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/4 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #5 # and #9 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #96 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #2 #. 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?
- Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7