Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #96 #, how long are the other two sides?

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Answer 1 · 2017-12-10T12:59:24

The other two sides are 4.6189 long each

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

#sin A = h / AD#
Given #AD = 12, sin A = sin (pi/3) = 1.732#

#h = AD * sin A = 12 * (1.732 )= 20.784#

Area of parallelogram = AB * h = 5
#:. AB = 96 / 20.784 = 4.6189#

The other two sides are #4.6189 # long each