This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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To find the speed of ship B, we need to use trigonometry based on the given bearings and distances. Step 1: Sketch the situation and determine the angles in the triangle formed by the port (P) and the positions of ships A and B after one hour (A' and B'). Let P be the port. After 1 hour: • Ship A is at A'. Distance PA' = Speed of A × Time = 10 km/h × 1 h = 10 km. • Ship B is at B'. Distance PB' = Speed of B × Time = Speed of B × 1 h. Let PB' = x km. The bearings are measured clockwise from the North line. • Bearing of A from P is 104^. • Bearing of B from P is 160^. The angle A'PB' (the angle at the port P) is the difference between these two bearings: A'PB' = 160^ - 104^ = 56^ Step 2: Determine the angle PA'B' (the angle at A'). Draw a North line at P and a parallel North line at A'. • The bearing of A' from P is 104^. • The back bearing of P from A' is 104^ + 180^ = 284^. This is the angle from the North line at A', clockwise to the line A'P. • The bearing of B' from A' is given as 215^. This is the angle from the North line at A', clockwise to the line A'B'. The angle PA'B' is the difference between the bearing of P from A' and the bearing of B' from A': PA'B' = 284^ - 215^\