Calculate Total Boat Trip Distance: 70° & 272° Directions

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SUMMARY

The discussion focuses on calculating the total distance a boat travels given its directional movements of 70° and 272°, ultimately docking 150 km north of its starting position. The Sine Law is identified as the primary mathematical tool for solving this problem. Participants emphasize the importance of accurately representing angles measured clockwise from north to correctly visualize the boat's path. A correct diagram is essential for applying the AAS (Angle-Angle-Side) method to find the total distance traveled.

PREREQUISITES
  • Understanding of trigonometric principles, specifically the Sine Law.
  • Ability to interpret angles in navigation, particularly in a clockwise format from north.
  • Familiarity with vector representation of movements in a two-dimensional plane.
  • Basic knowledge of geometric diagramming techniques.
NEXT STEPS
  • Study the application of the Sine Law in non-right triangles.
  • Learn how to accurately represent navigational angles in diagrams.
  • Explore vector addition and its relevance in calculating distances in navigation.
  • Review the AAS method for solving triangle problems in trigonometry.
USEFUL FOR

Students studying trigonometry, navigators, and anyone involved in maritime navigation or geometry-related problem-solving.

FrostScYthe
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Homework Statement


A boat leaves the dock and sails in a direction of 70°. Once reaching its destination on the opposite shore, it sails
in a direction of 272° and docks 150 km north of its original starting position. What is the total distance the boat
has traveled?

Homework Equations


Sine Law


The Attempt at a Solution


I don't think I'm getting the right answer because I'm not representing the problem correctly. This is how I'm representing the problem then I just simply use AAS

http://img243.imageshack.us/my.php?image=untitledce7.jpg
 
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Your angles are incorrect- they should be measured from north in a clockwise direction. Using this, you should be able to draw the correct diagram, where the final poistion is due north of the starting position.
 
I assume the 272° is with respect to the 'horizontal axis'?
 

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