Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #8 #, how long are the other two sides?

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Answer 1 · 2017-12-10T12:25:58

The other two sides are 5.226 long each

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#/_A+ /_B= pi#
#/_B= (7pi)/8#
#:./_A= pi - (7pi)/8 = pi/8#

#sin A = h / AD#
Given #AD = 4, sin A = sin (7pi/8) = 0.3827#

#h = AD * sin A = 4 * (0.3827 )= 1.5308#

Area of parallelogram = AB * h = 1.5308
#:. AB = 8 / 1.5308 = 5.226#

The other two sides are #5.226 # long each