Math Problem Statement
A ship sailed 3 km west, then 2 km south. Give its three-figure bearings from an observer who stayed at its starting point, correct to the nearest degree. b For a person on the ship, what would be the three-figure bearings looking back to the starting point?
Solution
Part (a): Bearings from the Starting Point
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Determine the Final Position of the Ship:
- The ship first sailed 3 km west, then 2 km south.
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Calculate the Angle of the Bearing:
- The bearing is measured clockwise from the north direction.
- The ship's final position is to the southwest of the starting point.
- This angle is measured from the westward direction toward the south, so the bearing from the north direction is:
- To the nearest degree, the bearing from the starting point is 214°.
Part (b): Bearings from the Ship Back to the Starting Point
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Determine the Bearing from the Ship:
- To find the bearing looking back to the starting point, you simply add to the bearing found in part (a).
- Since bearings are given as three-figure numbers and within to , subtract from .
- So, the bearing looking back to the starting point from the ship is 034°.
Do you want more details or have any questions about these calculations?
Here are 5 related questions to explore further:
- What is the significance of three-figure bearings in navigation?
- How would the bearing change if the ship traveled east and then north instead?
- How does the Pythagorean theorem apply to find the direct distance between the start and end points?
- What would be the bearing if the ship sailed 5 km west and 5 km north?
- How are bearings used in aviation compared to marine navigation?
Tip: Always remember that bearings are measured clockwise from the north direction.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Bearings
Right Triangle
Formulas
tan(theta) = opposite / adjacent
Reverse Bearing = Original Bearing + 180° (mod 360°)
Theorems
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Suitable Grade Level
Grades 9-12
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