Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #32 #, how long are the other two sides?

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Answer 1 · 2017-12-09T11:44:16

The other two sides are 16 long.

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

#sin A = h / AD#
Given #AD = 4, sin A = sin (pi/6) = 1/2#

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

Area of parallelogram = AB * h = 32
#:. AB = 32 / 2 = 16#

The other two sides are #16 # long