# Lesson Notes By Weeks and Term - Junior Secondary School 2

BEARINGS

SUBJECT: MATHEMATICS

CLASS:  JSS 2

DATE:

TERM: 3rd TERM

REFERENCE

• WABP ESSENTIAL MATHEMATICS FOR JSS BK 2 BY A.J.S. OLUWASANMI
• NEW GENERAL MATHEMATICS BY J.B. CHANNON & ETAL

WEEK FOUR

TOPIC: BEARINGS

CONTENT:    i. Compass bearing

1. Three figure bearing

iii. Finding the bearing of a point from another

COMPASS BEARING

A bearing gives the direction between two points in terms of an angle in degrees. The two types of bearing are compass bearing and three- figure bearings.

The four major compass directions are North (N) South (S) East (E) and West (W)

In compass bearing, the angles are measured from north to south depending on which one is nearer

Apart from the four main points or directions, there are also four main secondary direction i.e. NE (north east), SE (south east), SW (south west), NW (north west). The angles between each point is 45o

Worked examples

Draw a sketch to show each of these bearings marketing the angles clearly.

1. a) N35oW      B. N70oE      C. S58o

Solution

1. N35oW means from N, measures 35o toward the W or 35oW of N

1. b) N700E means 70o toward E.

1. c) S58oW means from S measures 58o toward W.

1. State the compass direction of the following diagrams:
1. a)                         b)

Solution

In a), the direction start from a wrong point (W) instead of N, therefore,

90 – 18 = 72o

i.e. N72oW

In b), the direction starts from a wrong point (E) instead of S therefore:

90 – 55 = 35o i.e. S35oE

Evaluation: Class Work

Find the compass direction of point A from point O in these diagrams.

1. a)                         b)

c)

NGM BK CHAPTER 23, page 185 – 187

Essential Mathematics for JSS BK 2, CHAPTER 24, pg 246-247

THREE-FIGURE BEARINGS

Three-figure bearings are given as the number of degrees from north, measured in a clockwise direction. Any direction can be given as a three figure bearing. Three digit are always given but angles less than 100o need extra zero to be written in front of the digits e.g. 008o, 060o, 070o up to 099o

Worked Examples

Find the three figure bearings of A, B, C, and D from X.

Solution

1. The arrow N shows the direction N, NXA = 63o. the bearing of A from X is 063o
2. NXB = 180 – 35 = 145o. The bearing of B from X is 145o
3. NXC clockwise = 180 + 75 = 255o. The bearing of C from X is 255o
4. NXD clockwise = 360 – 52 = 308o. The bearing of D from X is 308o.

Evaluation:

In the figure below, find the bearings of A, B, C and D from X.

Reference

NGM Bk. 2 Chapter 23, page 180 – 190.

To find the bearing of B from A

By constructing line N2A

2BA is 57o, similarly, N1AB = 57o (alternate angles are equal). From point A, starting from the North,

180 + 57 = 237o

1. The bearing of B from A is 237o
2. The bearing of A from B is 057o
1. The bearing of X from Y is 3190. Calculate the bearing of Y from X.
2. In each diagram, calculate i) the bearing of B from A and ii) the bearing of A from B.

GENERAL EVALUATION

From a point P the bearing of a house is 060o. From a point Q 100m due east of P, the bearing is 330o.

Draw a labeled sketch to show the positions of P, Q and the house.

REVISION QUESTION

1. A girl is facing East. If she turns clockwise through 2 right angles, then the direction she would be facing is ……………………..
2. A student is facing South East. If he turns anticlockwise through 1800, then the direction he would be facing is …………………..

WEEKEND ASSIGNMENT

1. The bearing of X from Y is 196o. The bearing of Y from X is     A. 016o       B. 074o      C. 106o     D. 196o
2. A boat sails on a bearing of 225o. Using compass bearing, in what direction is the boat sailing?     A. South East     B. North East     C. South West     D. North West
3. The bearing of point A from B is 058o. Find the bearing of point B from point    A. 058o     B. 122o     C. 3020     D. 238o
4. Which of the following statements is not true when we specify a direction with bearing?   A. Measure the angle from North   B. Measure anticlockwise     C. Measure clockwise     D. Always use three digits
5. In the diagram below, which of the following angles is the bearing of P from Q?   A. 065o    B. 2450     C. 295o     D. 115o