04Gbearings

toc = Bearings =

Compass Rose
You should be familiar with the directions of the compass.

A drawing like this showing the directions is called a ** compass rose **.

This one is an 8 point compass rose.

Note: Traditionally, North is drawn pointing up the page.

Compass directions like these are useful for general descriptions, but more accurate directions are needed in areas like navigation and surveying.

Note: ** Due North ** means the direction exactly North. Similarly, ** due South ** means directly to the south.

True Bearings

 * True bearings ** are the angle measured __clockwise__ around from North.
 * Always write True (or sometimes just T) after the angle (eg 140º True, eg 175ºT)
 * Put 0 before 2 digit angles so that it is always a 3 digit number (eg 045º True, eg 006ºT)



Compass Bearings
Each compass bearing:
 * Compass bearings ** are the angle measured from either North or South (whichever is closest).
 * start with **N** or **S**
 * then the angle from the North-South line
 * then **E** or **W** (depending which side of the North-South line)
 * Put 0 before 1 digit angles so that it is always a 2 digit number (eg N05ºW)



** Example 1 **
Write the bearings shown as:
 * 1) True Bearings
 * 2) Compass Bearings

__**Solution:**__

**(a)**
 * 1) 95º T
 * 2) S85ºE


 * (b) **
 * 1) 225º T
 * 2) S45ºW

** Example 2 **
A campsite is on a road that runs due East-West. A hiker leaves the camp on a bearing of 32º True and walks for 8.4 km to a lookout point. (a) How far due South does the hiker have to walk from the lookout point in order to find the road? (b) How far does the hiker have to walk along the road in order to return to the campsite?

__**Solution:**__

**(a)** {Draw a diagram} Let d = distance from the lookout point to the road

{from the diagram, use __**sin**__:}
 * q = 58º,
 * HYP = 8.4,
 * OPP = d

math \\ . \qquad \sin \big( \theta \big) = \dfrac{\text{OPP}}{\text{HYP}} \\. \\ . \\ . \qquad \sin \big( 58 \big) = \dfrac{d}{8.4} \\. \\ . \qquad d = 8.4 \times \sin \big( 58 \big) \\. \\ . \qquad d = 7.12 \text{ km} math

The hiker would have to walk 7.12km due South to meet the road.


 * (b) **

Let a = distance along road

{Using Pythagoras} math \\ . \qquad a^2 = c^2 - b^2 \\. \\ . \qquad a^2 = 8.4^2 - 7.12^2 \\. \\ . \qquad a^2 = 19.8656 \\. \\ . \qquad a = \sqrt{19.8656} \\. \\ . \qquad a = 4.46 \text{ km} math

The hiker would have to walk 4.46 km due West to return to camp. Go to top of page flat

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