The approximate corresponding height of the parallelogram is 4.8 units.
Height of the parallelogram
Given:
AB = 8.6
Coordinates
A(1, 3), B(8, 8), C(12, 5) and D(5, 0)
Hence:
Angle AB and AD
Slope m(AB)=8-3/8-1
Slope m(AB)=5/7
Slope m(AD) =3-0/1-5
Slope m(AD)=3/4
TanФ=5/7-(-3/4)÷1+(5/7) (-3/4)
TanФ=41/13
TanФ=3.154
Ф=tan^-1 (3.154)
Ф=72.41°
Angle ABE
Sin 72.41°=DE/5
0.95324=DE/5
Cross multiply
DE=5×0.95324
DE=4.76
DE=4.8 units (Approximately)
Therefore the correct option is C.
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