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 #42 #, how long are the other two sides?

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Answer 1 · 2017-12-10T13:38:26

The other two sides are 6.9284 long each

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#/_A+ /_B= pi#
#/_B= (2pi)/3#
#:./_A= pi - (2pi)/3 = pi/3#

#sin A = h / AD#
Given #AD = 7, sin A = sin (pi/3) = 0.866#

#h = AD * sin A = 7 * (0.866 )= 6.062#

Area of parallelogram = AB * h = 42
#:. AB = 42 / 6.062 = 6.9284#

The other two sides are #6.9284 # long each