Trigonometry

We can use the sine rule and cosine rule to calculate lengths and angles in non-right-angled triangles.  Although a perpendicular angle and therefore the hypotenuse are missing in these triangles, the sine and cosine rules are still based upon right-angled-trigonometry.  Are you able to give proof for both rules?  In what way do the two marines in the picture use trigonometry to calculate their position?