Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #48 #, how long are the other two sides?

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Answer 1 · 2018-02-28T06:40:16

Other two sides are of length #color(green)(a = 2 sqrt3# #units#

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

Given #b = 16, theta = pi / 3, A = 48#

#16 * a sin (pi/3) = 48#

#a = cancel(48)^color(brown)(3) / (cancel16 * sin(pi/3)#

#=> 3 / (sqrt3 / 2) = 2sqrt3#

Other two sides are of length #color(green)(a = 2 sqrt3# units