Two opposite sides of a parallelogram each have a length of #24 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #120 #, how long are the other two sides?

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Answer 1 · 2018-02-09T16:06:01

Other two sides are #color(green)(5.1764)# each approx.

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

Given #A_p = 120, theta = (5pi)/12 = 75^0, b = 24#

To find a.

#a = A_p / (b sin theta) = 120 / (24 * sin ((5pi)/12)) ~~ color(green)(5.1764#