# Two opposite sides of a parallelogram have lengths of #7 #. If one corner of the parallelogram has an angle of #pi/12 # and the parallelogram's area is #16 #, how long are the other two sides?

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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 the product of the base and the height. Let's denote the length of one of the other sides as ( b ) and the height as ( h ).

Given: Length of one side = 7 Area = 16 Angle = ( \frac{\pi}{12} )

Using the formula ( Area = base \times height ), we have: [ 16 = 7 \times h ]

Solve for ( h ): [ h = \frac{16}{7} ]

Now, the height ( h ) can be calculated using the trigonometric relationship: [ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} ] [ \tan\left(\frac{\pi}{12}\right) = \frac{h}{7} ]

Solve for ( h ): [ h = 7 \times \tan\left(\frac{\pi}{12}\right) ]

Once you find the value of ( h ), you can use it to calculate the length of the other side ( b ) using the Pythagorean theorem, since the triangle formed by the height, one side, and the diagonal is a right triangle.

[ b = \sqrt{(7)^2 + (h)^2} ]

Calculate ( b ) using the value of ( h ) obtained earlier.

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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.

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