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 #81 #, how long are the other two sides?

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Answer 1 · 2018-01-17T13:21:48

Length of the other two sides #a ~~ color (purple)(9.7415)#

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Area of parallelogram #A = b * h = b * a sin theta#

Given #A = 81, b = 9, theta = (3pi)/8#

#a = A / ( b * sin theta) = (cancel(81) 9)/ (cancel(9) * sin ((3pi)/8)#

Length of the other two sides #a = 9 / sin ((3pi)/8) ~~ color (purple)(9.7415)#