Answer
a. 2094 mi
b. No.
Work Step by Step
See sketch below
a.
$\displaystyle \tan 0.5^{o}=\frac{x}{240,000} \ \Rightarrow \ x=240,000\cdot\tan 0.5^{o}$
$ x\approx$ 2094.44826978$\approx $2094 miles
b.
The beam diverges more than 1000 miles.
It will not strike the moon.
