Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #54 #, how long are the other two sides?

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Answer 1 · 2018-02-07T09:14:15

Other two sides are #color(green)(6sqrt3# units long

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Given : #Area, A = 54, theta = pi/3, b = 6#

To find a.

#b * a sintheta = A#

#6 * a sin(pi/3) = 54#

#a = 54 / (6 * sin(pi/3) )= (cancel(54)^9 * 2) / (cancel6 * sqrt3) = 18/sqrt3 = color(green)(6sqrt3# units