Two opposite sides of a parallelogram each have a length of #14 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #70 #, how long are the other two sides?
Length of other two sides **=5.7735#
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To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by ( \text{Area} = \text{base} \times \text{height} ).
Given that one corner of the parallelogram has an angle of ( \frac{2\pi}{3} ), we can use trigonometric properties to determine the height of the parallelogram. Since the opposite sides are equal in length and form a right angle with each other, the height of the parallelogram is equal to one of these sides times the sine of the given angle.
Let's denote the length of one of these sides (the height) as ( h ). Then, using the sine of ( \frac{2\pi}{3} ), which is ( \frac{\sqrt{3}}{2} ), we have ( h = 14 \times \frac{\sqrt{3}}{2} ).
Now, we can find the length of the other two sides by dividing the area of the parallelogram by the height we just calculated:
[ \text{Area} = 70 = \text{base} \times \text{height} ] [ 70 = \text{base} \times \left(14 \times \frac{\sqrt{3}}{2}\right) ]
Solving for the base:
[ \text{base} = \frac{70}{14 \times \frac{\sqrt{3}}{2}} ]
[ \text{base} = \frac{70 \times 2}{14 \times \sqrt{3}} ]
[ \text{base} = \frac{140}{14\sqrt{3}} ]
[ \text{base} = \frac{10}{\sqrt{3}} ]
Now, since the opposite sides of a parallelogram are equal in length, the lengths of the other two sides are also ( 14 ).
Therefore, the lengths of the other two sides of the parallelogram are ( \frac{10}{\sqrt{3}} ) and ( 14 ).
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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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