Yacht Navigation

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Dec 4, 2021.

  1. nycmathguy

    nycmathguy

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    Section 4.8

    20211127_143925.jpg

    IMG_20211204_184121.jpg

    You say?
     
    nycmathguy, Dec 4, 2021
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  2. nycmathguy

    MathLover1

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    a and b are correct

    c. bearing should be 180-1.4=178.6 degrees
     
    MathLover1, Dec 5, 2021
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  3. nycmathguy

    nycmathguy

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    For part (c), where did 180 degrees come from? Can you draw the correct geometric figure to illustrate all points of interest?
     
    nycmathguy, Dec 5, 2021
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  4. nycmathguy

    MathLover1

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    upload_2021-12-5_8-43-14.jpeg so, 180-1.4 degrees
     
    MathLover1, Dec 5, 2021
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  5. nycmathguy

    nycmathguy

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    I thought S 1.3° E means to start on the South line and navigate towards the East. Doesn't the letter S in S 1.4° E means to start on the South line? Are you saying that no matter what bearing is given, we always begin on the North line in terms of rotation?
     
    nycmathguy, Dec 5, 2021
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  6. nycmathguy

    MathLover1

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    REMEMBER: Bearings are always measured clockwise from North and are given as 3 digits.

    examples:
    [​IMG]If you walk from O in the direction shown by the red arrow, you are walking on a bearing of 110 °.

    [​IMG]

    Note that the first two bearings above are in directly opposite directions to each other.
    They have different bearings, but they are exactly 180° apart as they are in opposite directions.
    A line in the opposite direction to the third bearing above would have a bearing of 150° because 330° - 180° = 150°.
     
    MathLover1, Dec 5, 2021
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  7. nycmathguy

    MathLover1

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    Example 2
    A ship sails from A to B on a bearing of 120°.
    [​IMG]
    On what bearing will it have to sail to return from B to A?

    We can extend the line from A to B, then rotate through 180° to head in the opposite direction.
    [​IMG]

    We can see from the diagram above that the bearing from B to A is 300°, because 120° + 180° = 300°.

    REMEMBER: Bearings in exactly opposite directions are called back bearings and are always 180° apart.
     
    MathLover1, Dec 5, 2021
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  8. nycmathguy

    nycmathguy

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    Amazing as always. Great drawings. Thanks.
     
    nycmathguy, Dec 5, 2021
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