Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #24 #, how long are the other two sides?

1 Answer
Sep 11, 2016

4

Explanation:

#A = bh#

#A = 24#
#b = 12#
#=> h = 2#


#pi = 180^o#

#=> 5pi/6 = 150^o#

Since we are dealing with a parallelogram, adjacent interior angles have a sum of #180^o#

#=># other interior angle is #30^o#

If we draw an imaginary segment connecting the bases, we will have a 30-60-90 triangle with the side opposite #30^o# having a length of 2 (i.e. the parallegram's height) and the hypotenuse being the parallelogram's other side.

The sides of a 30-60-90 triangle have the ratio #1:sqrt3:2#.
Since the side opposite #30^o# is 2, the hypotenuse should be 4.