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.
