#### Answer

The length of the shadow is $\approx 8.4$ ft.

#### Work Step by Step

Refer to the attachment:
1. Find the two missing angles in $\triangle ABC$
$\angle A = 90^{\circ} $(Given as a right angled triangle)
$\angle B = 90 - 55 = 35^{\circ} $
$\angle C = 55^{\circ}$ (Alternate angles)
2. Use the sine law to solve for $x$
$\frac{x}{sin35} = \frac{12}{sin55}$
$ x = \frac{12sin35}{sin55}$
$ x = \frac{6.883...}{0.819...}$
$ x = 8.402... $ft
$ x \approx 8.4 $ft