Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #44 #, how long are the other two sides?

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Answer 1 · 2017-12-10T12:21:37

Other two sides are 11 long each

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#/_A+ /_B= pi#
#/_B= (5pi)/6#
#:./_A= pi - (5p)/6 = pi/6#

#sin A = h / AD#
Given #AD = 8, sin A = sin (pi/6) = 0.5#

#h = AD * sin A = 8 * (1/2 )= 4#

Area of parallelogram = AB * h = 44
#:. AB = 44 / 4 = 11#

The other two sides are #11 # long each