10.5A Directions and Bearings

Distance and Bearings

In navigation and surveying, the direction or bearing from point 0 to point P equals the acute angle between the ray OP and the vertical line, the north-south line.

These rules must be followed

1. Start using the y-axis ... NORTH/SOUTH

2. Include the following parts

a. Direction (N, S).

b. An acute angle.

c. Direction (E, W)

d. example: N45°E

To help you remember the locations of N, S, E, and W using directions for driving in Chicagoland.

North - Cubbies

South - Sox

East - Lake

West - Suburbs

Imagine you are traveling N45°W -

in what quadrant are you traveling? (Q2)

If you were told to go S20°W -

in what quadrant are you traveling? (Q3)

Remember

~ Always use the vertical North/South line (y-axis) to determine the angle and the direction.

~ The bearing angle will always bounce off the North/South line and will be either to the right or left of this vertical line.

~ When working with triangles, it is very seldom that the bearing angle will be one of the triangle's angles.

~ You will be applying what you know about supplementary angles as you solve the problem.

Direct directions of DUE North, DUE South, DUE East, or DUE West use

~ The x-axis (west and east)

~ The y-axis (north and south)

Example Word Problems (These will be assigned in a later assignment)

1. Town B is 26 miles from town A at a bearing of S15°W.

Town C is 54 miles from town A at a bearing of S7°E.

Compute the distance from town B to town C.

Round answer to the nearest mile.

2. Town C is 5 miles due east of town D.

Town E is 12 miles from town C at a bearing (from C) of N52°E.

How far apart are towns D and E?

Round to the nearest mile.

3. A small fire is sighted from ranger stations A and B.

The bearing of the fire from station A is N35°E, and the bearing of the fire from station B is N49°W.

Station A is 1.3 miles due west of station B.

How far is the fire from each ranger station?

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