# Two opposite sides of a parallelogram each have a length of 7 . If one corner of the parallelogram has an angle of (2 pi)/3  and the parallelogram's area is 28 , how long are the other two sides?

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May 22, 2018

Other two sides are $4.62$ unit long.

#### Explanation:

The area of the parallelogram is ${A}_{p} = {s}_{1} \cdot {s}_{2} \cdot \sin \theta$

Where s_1=7,s_2=?,theta=(2 pi)/3=120^0  are the adjacent

sides and corner angle respectively.

${A}_{p} = 28 \therefore 28 = 7 \cdot {s}_{2} \cdot \sin 120 \mathmr{and} {s}_{2} = \frac{28}{7 \cdot \sin 120}$ or

${s}_{2} \approx 4.62 \left(2 \mathrm{dp}\right)$ unit.

Other two sides are $4.62$ unit long. [Ans]

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