#### Answer

The distance from the assigned target would be 34.0 miles.

#### Work Step by Step

We can convert the angle of error to degrees:
$\theta_e = 30'' = \frac{30}{3600}^{\circ} = \frac{1}{120}^{\circ}$
We can use the earth-moon distance $d$ to find the distance $x$ from the assigned target:
$\frac{x}{d} = tan~\theta_e$
$x = (d)~tan~\theta_e$
$x = (234,000~mi)~tan~(\frac{1}{120})^{\circ}$
$x = 34.0~mi$
The distance from the assigned target would be 34.0 miles.