Two opposite sides of a parallelogram each have a length of #36 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #64 #, how long are the other two sides?

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Answer 1 · 2016-12-15T21:44:48

#~~1.84#

Here's a demonstration for the problem
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We need to find the length #b# in this problem

#sin((5pi)/12)=h/36#

#h=36sin((5pi)/12)#

To get an accurate solution we won't evaluate #h# until the last step

The area of parallelogram is given by #->color(red)A=bcolor(blue)h#

#color(red)A=color(red)64# and #color(blue)h=color(blue)(36sin((5pi)/12))#

#color(red)64=b*color(blue)(36sin((5pi)/12))#

#b=color(red)64/color(blue)((36sin((5pi)/12)))#

#b~~1.84#