Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #48 #, how long are the other two sides?

Question

Two opposite sides of a parallelogram each have a length of #12  #.  If one corner of the parallelogram has an angle of #( pi)/3   # and the parallelogram's area is #48      #, how long are the other two sides?

Aurora Ayala · Accepted Answer

#=4.62# Area#=ab sin theta# where #a=12# and #theta=pi/3#; we have to find #b=?# So Area #=48=12 b sin(pi/3)# or #12 b sin(pi/3)=48# or #b sin(pi/3)=48/12# or #b(0.866)=4# or #b=4/0.866# or #b=4.62#

Savannah Aguilar · Answer

undefined To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram: Area = base × height. Since we know the area is 48 and one of the sides (base) is 12, we can solve for the height.

Area = base × height
48 = 12 × height
height = 48 / 12
height = 4

Now, we have the height of the parallelogram. Since opposite sides of a parallelogram are equal in length, the other side opposite to the given base will also be 12 units long.

So, the lengths of the other two sides of the parallelogram are both 12 units.