Two opposite sides of a parallelogram each have a length of #25 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #175 #, how long are the other two sides?

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Answer 1 · 2017-09-14T10:58:47

Other two sides are # 7.25# unit each .

Opposte sides of parallelogram is # s_1=25#

Angle of one corner of the parallelogram is

# /_theta = (5pi)/12=(5*180)/12=75^0# and

Area of parallelogram is # A_p=175 #

We know area of parallelogram is # A_p=s_1*s_2*sin theta # ,

where #s_2# is the adjacent side of sides #(s_1)#

#:. 175 =25*s_2*sin 75:. s_2= 175/(25*sin75) # or

#s_2= 175/(25*sin75) ~~ 7.25(2p)# unit

Other two sides are # 7.25(2p)# unit each . [Ans]