Problem
Problem
A helicopter A observes two ships B and C. B is 23.8 km from the helicopter and C is 31.9 km from it. The angle of view from the helicopter to B and C, is . How far are the ships apart?Intuitive explanation
You're using the Law of Cosines to find a missing side in a triangle when you know two sides and the included angle between them. The helicopter is at the apex, and the two ships form the other vertices—think of it as the triangle's "opposite side" problem. Once you identify which side is opposite the known angle, the Law of Cosines lets you solve for the distance directly without needing any other angles.
Intuitive explanation
You're using the Law of Cosines to find a missing side in a triangle when you know two sides and the included angle between them. The helicopter is at the apex, and the two ships form the other vertices—think of it as the triangle's "opposite side" problem. Once you identify which side is opposite the known angle, the Law of Cosines lets you solve for the distance directly without needing any other angles.