To solve the problem, we need to analyze the situation using basic trigonometry. The bearing of 165° indicates the direction in which the ship is sailing relative to true north.
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Understanding Bearings: A bearing of 165° means that the direction is 165 degrees clockwise from the north (which is 0°). This means the direction is slightly more towards the south-east than directly south.
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Calculating the Southern Component: To find the southward distance from point A to point B, we can use trigonometric functions. If we denote \(d\) as the distance from A to B, the southward component can be calculated as:
\[ \text{South component} = d \cdot \cos(15°) \] Here, \(15°\) is derived from \(180° - 165°\) since we are interested in the angle from the south line.
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Calculating the Eastward Component: If needed, to analyze the eastward component, it would be:
\[ \text{East component} = d \cdot \sin(15°) \]
However, since the problem only asks for the distance to point B south of point A, we focus on the south component.
Conclusion:
To determine how far point B is south of point A, you need the distance \(d\) from A to B. If you have a specific value for \(d\), you can substitute that into the equation:
\[ \text{South component} = d \cdot \cos(15°) \]
If you provide a distance \(d\), I can calculate the exact south component for you.