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

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Answer 1 · 2017-12-12T07:21:31

The other two sides are 3.464 long each

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

#sin A = h / AD#
Given #AD = 14, sin A = sin ((pi)/3) = 0.866#

#h = AD * sin A = 14 * (0.866 )= 12.124#

Area of parallelogram = AB * h = 42
#:. AB = 42 / 12.124 = 3.464#

The other two sides are #3.464 # long each