Finding a Course Angle

Navigation also runs the other way: the distances are known from a chart and the angle to steer is wanted. That is SSS, an angle from the law of cosines, then a bearing from the angle.

From a harbour H, a buoy B is 20 km away and an island I is 14 km away, and the buoy and the island are 9 km apart. The angle φ at H between them: ${9}^{2} = {20}^{2}+{14}^{2}-2\cdot 20\cdot 14\cdot \cos\left(\varphi\right)$, so cos φ = 515/560 and φ is about 23.13°. If the buoy is on bearing 080° and, looking from H, the island lies to the left of it, the island is on bearing 080° − 23.13° ≈ 056.87°.