## Trigonometry (11th Edition) Clone

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.