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

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Answer 1 · 2018-02-20T01:59:43

Other two sides are #color(brown)(a = A / (b sin theta) = 13.8564# units long

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

Given : #b = 6, theta = pi/3, A = 72#

To find a

#a = A / (b sin theta) = 72 / 6 sin (pi/3)#

#a = cancel(72)^color(red)(12) / (cancel6 * (sqrt3/2))#

#color(brown)(a = (12 * 2)/sqrt3 = 8 sqrt3 = 13.8564# units