Question

You found a treasure map, and it's said: staring at well walk 30 m north, 20 m 30° N of East, 15 m 18° south of west, and finally 10 m north. How far is the treasure map from the well?

Answer 1

$$d_x=20\cos 30^{\circ}-15\cos 18^{\circ}=3.0\:{\rm m}\\ d_y=30+20\sin 30^{\circ}-15\sin 18^{\circ}+10=45.4\:{\rm m}$$

So, the distance to the treasure from the well

$$d=\sqrt{d_x^2+d_y^2}=\sqrt{3.0^2+45.4^2}=45.5\:\rm m$$