Two opposite sides of a parallelogram each have a length of #18 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #160 #, how long are the other two sides?

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Answer 1 · 2017-12-10T13:24:08

The other two sides are 9.2027 long each

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#/_A+ /_B= pi#
#/_B= (5pi)/12#
#:./_A= pi - (5pi)/12 = (7pi)/12#

#sin A = h / AD#
Given #AD = 18, sin A = sin ((7pi)/12) = 0.9659#

#h = AD * sin A = 18 * (0.9659 )= 17.3862#

Area of parallelogram = AB * h = 5
#:. AB = 160 / 17.3862 = 9.2027#

The other two sides are #9.2027 # long each