Yacht Navigation

[nycmathguy]

Section 4.8

You say?

 

[MathLover1]

a and b are correct

c. bearing should be 180-1.4=178.6 degrees

 

[nycmathguy]

a and b are correct

c. bearing should be 180-1.4=178.6 degrees

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

 

[MathLover1]

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

so, 180-1.4 degrees

 

[nycmathguy]

View attachment 1201 so, 180-1.4 degrees

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?

 

[MathLover1]

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

examples:

If you walk from O in the direction shown by the red arrow, you are walking on a bearing of 110 °.

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]

Example 2
A ship sails from A to B on a bearing of 120°.

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.

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.

 

[nycmathguy]

Example 2
A ship sails from A to B on a bearing of 120°.

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.

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.

Amazing as always. Great drawings. Thanks.