Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #18 #, how long are the other two sides?

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Answer 1 · 2017-07-08T10:02:08

#"Missing side" = 2.31#

#((2pi)/3)^"c"=60^circ#

If the whole area is made of two equal triangles, and has an area of 18 in total, then the area of one triangle is #18/2=9#

Area of a triangle #=((a*b*sin(C))/2)#, where #a# and #b# are two sides, and #C# is the angle directly opposite to the unknown side.

In this case, #"Area of triangle" = 9 = (a*9*sin(60))/2#, then #a=18/(9sin(60))=2/sin(60)=2.31 ("rounded to 2 d.p.")#