Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #26 #, how long are the other two sides?

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Answer 1 · 2017-12-10T13:11:52

The other two sides are 3.1268 long each

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#/_A+ /_B= pi#
#/_B= (3pi)/8#
#:./_A= pi - (3pi)/8 = (5pi)/8#

#sin A = h / AD#
Given #AD = 9, sin A = sin ((5pi)/8) = 0.9239#

#h = AD * sin A = 9 * (0.9239 )= 8.3151#

Area of parallelogram = AB * h = 5
#:. AB = 26 / 8.3151 = 3.1268#

The other two sides are #3.1268 # long each