Lesson Notes By Weeks and Term - Junior Secondary School 3

SUBJECT: MATHEMATICS

CLASS:  JSS 3

DATE:

TERM: 2nd TERM

 
WEEK NINE                                                                                    DATE--------------

TOPIC: BEARING

BEARING

CONTENT:      i)   Compass bearing

1. ii)   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 bearings are compass bearings and three figure bearings.

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

    N

    W        E

                                                 S   

In compass bearings, the angles are measured from North or South depending on which one is nearer

                                       NE    N           NE

                             W                                              E

                                  SW               S           SE   

Apart from the four main points or directions, there are also four main secondary directions i.e NE (North East), SE (South East), SW (South West), NW (North West). The angle between each point is 450.

Worked Examples

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

1. a) N 350 W     b) N 700 E      c) S 580

Solution

1. a) N 350 W means from N, measures 350 towards the W or 350 W of N.

    N 350 W            N

1. b) N 700 E means 700 towards E.

                                                      N

        N 700 E

                                          W                        E

1. c) S 580W means from S measures 580 towards W.

                                                     N

                                   W                                         E

                                                      S

    S580W

Evaluation:

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

1. a) N b)

    N

        W                                     E                            W                                      E

                          S                                                                     S

1. c) N

                       W                                     E

                        S   

REFERENCE

NGM Bk 2 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 digits are always given but angles less than 1000 need extra zero to be written in front of the digits e.g. 0000, 0360, 0700 up to 0990.

Worked Examples

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

                                   N           A

                     D          

          W                          X                            E

                C                   

                                    S        B   

Solution

630. a) The arrow N shows the direction N, NXA = 630. The bearing of A from X is 0630.
631. b) NXB = 180 – 35 = 1450. The bearing of B from X is 1450.
632. c) NXC clockwise = 180 + 75 = 2550. The bearing of C from X is 2550.
633. d) NXD clockwise = 360 – 52 = 3080. The bearing of D from X is 3080.

Evaluation

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

                                D            N          A

    W                       X           E

                             C          

                                               S       B

                                          N2                              A

                                                                       570          

                                            570 

                                          B                             N1

By constructing line N2A

2BA is 570, similarly, N1AB = 570 (alternate angles are equal). From point A, starting from the North, 180 + 57 = 2370.

1. a) The bearing of B from A is 2370
2. b) The bearing of a from B is 0570.

Evaluation: 

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

    N2

1. a) b)     A   1500 N1

N2                                                                                                                                                                            B

                                                B

   2500   A   

READING ASSIGNMENT

NGM Bk 2 Chapter 23, Page 189 – 190

Essential Mathematics for JSS Bk 2, Chapter 24, Pg 248 - 250.

WEEKEND ASSIGNMENT

1. If the angle of elevation of P from Q is 380, then the angle of depression of Q from P is_____
2. a) 190   b) 520     c) 380     d) 1280
3. The compass direction of the diagram below is 

    N

    W    E

    S

1. a) S200W     b) S600W      c) S700     d) S200E
2. Use the diagram below to answer questions 3 to 5.

    N

I

    M

                                                                         K

    L   

    The bearing of J from X is ___________________

1. a) 610     b) 1030     c) 420     d) 1880
2. The bearing of L from X is _______________
3. a) 2600     b) 1600           c) 1000           d) 760
4. The bearing of M from X is ____________
5. a) 2260       b) 3000       c) 3360        d) 240

THEORY

1. Bala  stood on one side of a field and finds that the bearing of an orange trees is N75 0 W.

 Shortly after, Asiru moved to the foot of the orange tree to spot Bala. Calculate bala’s bearing from asiru.    X

2. The bearing of P from Q is 1950, what would be the bearing of Q from P?