Bearing and Distances

 

Welcome to Class !!

We are eager to have you join us !!

In today’s Mathematics class, We will be discussing Bearing and Distances. We hope you enjoy the class!

 

geometric construction mathematics classnotesng

CONTENT:  

  i. Compass bearing

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 bearing are compass bearing and three-figure bearings.

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

 

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

 

Worked examples

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

a) N35oW    (B) N70oE    (C.) S58oW

Solution

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

 

 

 

 

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.

 

Reading Assignment

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 Example

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 – 19

 

Evaluation

In each diagram below, calculate

i) the bearing of B from A

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 labelled 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 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? 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 058o     B. 122o     C. 3020     D. 238o
  4. Which of the following statements is not true when we specify a direction with bearing? 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? 065o    B. 2450     C. 295o     D. 115o

 

 

 

 

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about Statistics: Data Presentation. We are very much eager to meet you there.

 

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