Two opposite sides of a parallelogram each have a length of #2 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #8 #, how long are the other two sides?

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Answer 1 · 2017-11-20T17:08:18

See below.

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The area of a parallelogram is given by #A= bh#

We were given one of the obtuse angles. Since opposite angles are equal and all angles add up to #2pi#, we can find the acute angles.

Acute angle: #(2pi-((7pi)/8 + (7pi)/8))/2=pi/8#

#h=2sin(pi/8)~~0.7654#

Using #A=bh#

#8=0.7654b=>b=10.452#

( 3 .d.p.)