Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(11 pi)/12 # and the parallelogram's area is #42 #, how long are the other two sides?

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Answer 1 · 2017-12-10T13:50:07

The other two sides are 40.5719 long each

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#/_A+ /_B= pi#
#/_B= (11pi)/12#
#:./_A= pi - (11pi)/12 = pi/12#

#sin A = h / AD#
Given #AD = 4, sin A = sin (pi/12) = 0.2588#

#h = AD * sin A = 4 * (0.2588 )= 1.0352#

Area of parallelogram = AB * h = 5
#:. AB = 42 / 1.0352 = 40.5719#

The other two sides are #40.5719 # long each