A ship sails from A to B, 12 km on a bearing of 120°. It then sails west to C such that the bearing of C from A is 250°. Find the distance BC.

let's break down this bearing problem with a clear diagram and step-by-step calculations.

Problem Analysis:

• A ship starts at point A.
• It moves to point B, 12 km away, on a bearing of 120°.
• From B, it moves westwards to point C. This means the line segment BC is horizontal (constant latitude).
• The bearing of C from A is 250°.

Step 1: Draw the Diagram.

Let point A be the origin $(0,0)$. We'll use a coordinate system where North is the positive y-axis, East is the positive x-axis. Bearings are measured clockwise from North.