Two opposite sides of a parallelogram each have a length of #2 #. If one corner of the parallelogram has an angle of #(5 pi)/8 # and the parallelogram's area is #15 #, how long are the other two sides?

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Answer 1 · 2017-02-14T18:37:44

#S_2 ~~ 8.1" units"#

Given: #S_1 = 2" units", theta = (5pi)/8" radians", and A = 15" units"^2#

Let #h =# the height of the parallelogram # = S_1sin(theta)" [1]"#
Let #S_2 =# the unknown sides.

If we designate #S_2# as the base, then the equation for the area becomes:

#A = hS_2#

Solve for #S_2#

#S_2 = A/h" [2]"#

Substitute equation [1] into equation [2]:

#S_2 = A/(S_1sin(theta))" [3]"#

We know all of the values for the right side of equation [3]:

#S_2 = (15" units"^2)/((2" units")sin((5pi)/8))#

#S_2 ~~ 8.1" units"#