Bearings

Topic Content:

Bearings are angles measured in a clockwise direction from North . This system is used to describe the direction of a point or object relative to a reference point, typically North.

This north direction is usually provided in the maths exam question. We then measure the required angle in a clockwise direction. All bearings need to be given in three figures, e.g. 008°, 010°, 045°, 080°, 128°, 260°, etc.

For Example:

The diagram shows three points X , Y and Z .

The angles are measured clockwise from the north line. 

• The bearing of X from Z is 045º
• The bearing of Y from Z is 250º

Example 6.2.1:

The points X , Y and Z are located such that Y is 15 km south of X , Z is 20 km from X on a bearing of 270º.

Calculate, correct to:
(a) two significant figures,   |YZ|
(b) the nearest degree, the bearing of Y from Z

Solution

(a)

Using Pythagoras’ Theorem:

⇒ \(\scriptsize |YZ|^2 = 15^2 \: + \: 20^2  \\ \scriptsize = 225 \: + \: 400 \\ \scriptsize = |YZ|^2 = 625 \\\scriptsize = |YZ| = \sqrt{625} \\ \scriptsize|YZ| = 25 \: km \)

Answer ⇒   |YZ| = 25 km

(b)

To the nearest degree, the bearing of Y from Z

Solution