#### Answer

We calculate that the distance between Bochum and the moon is 419,000 km, which is similar to the known distance of 406,000 km

#### Work Step by Step

We can form a triangle with Bochum, Donaueschingen, and the moon. Let $D$ be the angle at Donaueschingen. Then $D = 180^{\circ}-52.7430 = 127.2570^{\circ}$
We can find the angle $M$ at the moon:
$B+D+M = 180^{\circ}$
$M = 180^{\circ}-B-D$
$M = 180^{\circ}-52.6997^{\circ}- 127.2570^{\circ}$
$M = 0.0433^{\circ}$
We can find the length of side $d$ which is the distance from Bochum to the moon:
$\frac{d}{sin~D} = \frac{m}{sin~M}$
$d = \frac{m~sin~D}{sin~M}$
$d = \frac{(398~km)~sin~(127.2570^{\circ})}{sin~(0.0433^{\circ})}$
$d = 419,000~km$
We calculate that the distance between Bochum and the moon is 419,000 km, which is similar to the known distance of 406,000 km.