Two opposite sides of a parallelogram each have a length of #24 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #54 #, how long are the other two sides?

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Answer 1 · 2017-12-10T13:58:39

The other two sides are 2.3294 long each

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

#sin A = h / AD#
Given #AD = 24, sin A = sin ((7pi)/12) = 0.9659#

#h = AD * sin A = 24 * (0.9659 )= 23.1816#

Area of parallelogram = AB * h = 5
#:. AB = 54 / 23.1816 = 2.3294#

The other two sides are #2.3294 # long each