Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #(5 pi)/8 # and the parallelogram's area is #64 #, how long are the other two sides?

Question

Two opposite sides of a parallelogram each have a length of #16  #.  If one corner of the parallelogram has an angle of #(5 pi)/8   # and the parallelogram's area is #64      #, how long are the other two sides?

Sadie Adams · Accepted Answer

The other two sides are #4.33(2dp)# unit long.

We know, the area of the parallelogram as #A_p=s_1*s_2*sin theta # Here #A_p=64 ; s_1=16 ; theta=(5*180)/8=112.5^0 :. s_2=A_p/(s_1*sin theta) = 64/(16 *sin112.5)=4.33(2dp)# The other two sides are #4.33(2dp)#unit long.[Ans]

Jayden Jackson · Answer

undefined To find the lengths of the other two sides of the parallelogram, given that two opposite sides have a length of 16 and the area is 64, and one angle is $ \frac{5\pi}{8} $, you can use the formula for the area of a parallelogram:

$$ \text{Area} = \text{base} \times \text{height} $$

In this case, since two opposite sides form a base, and the height is the perpendicular distance between these sides, you can find the height using trigonometry:

$$ \text{Height} = 16 \times \sin\left(\frac{5\pi}{8}\right) $$

Once you find the height, you can use it to calculate the lengths of the other two sides. Since the opposite sides of a parallelogram are equal in length:

$$ \text{Other side length} = \sqrt{16^2 - (\text{Height})^2} $$

Calculate the height using the given angle and then find the lengths of the other two sides using the formula above.