Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #30 #, how long are the other two sides?

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Answer 1 · 2016-10-10T04:51:52

#5.41#

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To solve this problem, we use a little trigonometry

#color(blue)("Area of parallelogram"=a*b*sin(C)#

Where,

#color(orange)("a and b are the sides"#

#color(orange)("C is the angle between them"#

As the area is #30#

#rarra*b*sin(C)=30#

#rarr6*x*sin(67.5)=30#

#rarr6*x*0.923=30#

#rarr5.54*x=30#

#rarrx=30/5.54#

#color(green)(rArrx=5.41#

Note: these are only approximations