Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #56 #, how long are the other two sides?

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Answer 1 · 2017-07-26T10:42:54

The other two sides are #36.58 (2dp) # unit long.

Area of parallelogram is #A=s_1*s_2*sin theta # , where

# s_1, s_2, theta # are the adjacent sides and corner angle of the

parallelogram. Here #s_1= 4 , A=56 , theta = (7pi)/8 = (7*180)/8#

#= 157.5 , s_2 = ? :. s_2 = A/(s_1sin theta) = 56/(4 * sin 157.5# or

#s_2= 14/sin 157.5 ~~ 36.58 (2dp) #

The other two sides are #36.58 (2dp) # unit long. [Ans]