Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #18 #, how long are the other two sides?

Question

1157 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-10T13:41:30

The other two sides are 5.226 long each

enter image source here
#/_A+ /_B= pi#
#/_B= (7pi)/8#
#:./_A= pi - (7pi)/8 = pi/8#

#sin A = h / AD#
Given #AD = 9, sin A = sin (pi/8) = 0.3827#

#h = AD * sin A = 9 * (0.3827 )= 3.4443#

Area of parallelogram = AB * h = 18
#:. AB = 18 / 3.4443 = 5.226#

The other two sides are #5.226 # long each