Types of Bearings Mathematics JSS 2 Third Term Mathematics Lesson Notes

Good day, class! Today, we will be discussing an important topic in mathematics called “bearings.” Bearings are used to describe the direction of one point or object in relation to another. They are often represented as angles measured in degrees, and they help us navigate and understand positions and directions.

There are two main types of bearings: true bearings and magnetic bearings. Let’s take a closer look at each of them:

1. True Bearings:
True bearings are measured with respect to the geographic north pole, also known as true north. In other words, they are based on the Earth’s rotational axis. True bearings are widely used in navigation, cartography, and surveying. The reference direction for true bearings is the north direction, which is assigned a bearing of 0 degrees. The other directions are measured clockwise from the north, ranging from 0° to 360°.

To represent a true bearing, we use three digits: the first digit represents the angle in tens, the second digit represents the angle in units, and the third digit represents the number of minutes. For example, a true bearing of 045° means the direction is 45 degrees clockwise from true north.

2. Magnetic Bearings:
Magnetic bearings, on the other hand, are measured with respect to the magnetic north pole. The Earth’s magnetic field influences these bearings. The magnetic north pole is not fixed and can change slightly over time due to the movement of the Earth’s magnetic field.

To work with magnetic bearings, we use a compass. The compass needle aligns itself with the Earth’s magnetic field, which allows us to determine magnetic bearings. Similarly to true bearings, magnetic bearings are measured clockwise from the reference direction, which is magnetic north.

Just like with true bearings, we represent magnetic bearings using three digits: the first digit represents the angle in tens, the second digit represents the angle in units, and the third digit represents the number of minutes. For example, a magnetic bearing of 315° means the direction is 315 degrees clockwise from magnetic north.

It’s important to note that when using bearings, we always measure the angle clockwise. So, if you’re given a bearing of 120°, it means you would move 120 degrees in a clockwise direction.

I hope this explanation helps you understand the different types of bearings. Remember, bearings are essential in navigation and provide us with valuable information about directions.

Worked Samples

1) If the bearing of A from B is 120°, what is the bearing of B from A?

Solution

If the bearing of A from B is 120°, we can determine the bearing of B from A by adding 180° to the given bearing. This is because the bearing of B from A is the opposite direction or the reverse of the bearing of A from B.

So, to find the bearing of B from A, we add 180° to 120°:

120° + 180° = 300°

Therefore, the bearing of B from A is 300°.

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2). If the bearing of Ibadan from Benin-City is 067°, what is the bearing of Benin-City from Ibadan

Solution

To find the bearing of Benin-City from Ibadan, we need to determine the opposite or reverse direction of the given bearing, which is 067°.

To obtain the reverse bearing, we add 180° to the given bearing:

067° + 180° = 247°

Therefore, the bearing of Benin-City from Ibadan is 247°.

3). If the bearing of Zaria from Okene is 115°, what is the bearing of Okene from Zaria?

Solution

To find the bearing of Okene from Zaria, we need to determine the opposite or reverse direction of the given bearing, which is 115°.

To obtain the reverse bearing, we add 180° to the given bearing:

115° + 180° = 295°

Therefore, the bearing of Okene from Zaria is 295°.

4). If the bearing of X from Y is 358°, what is the bearing of Y from X?

If the bearing of X from Y is 358°, to find the bearing of Y from X, we need to determine the opposite or reverse direction of the given bearing.

To obtain the reverse bearing, we subtract 180° from the given bearing:

358° – 180° = 178°

Therefore, the bearing of Y from X is 178°.

Evaluation

1. The reference direction for true bearings is __________.
a) South
b) West
c) North

2. Magnetic bearings are measured with respect to the __________.
a) Magnetic south pole
b) Geographic north pole
c) Magnetic north pole

3. A true bearing of 090° represents a direction that is __________.
a) Due north
b) Due south
c) Due east

4. If the bearing of A from B is 180°, the bearing of B from A is __________.
a) 180°
b) 90°
c) 0°

5. The bearing of Benin-City from Ibadan is 045°. The reverse bearing of Ibadan from Benin-City is __________.
a) 045°
b) 135°
c) 225°

6. The bearing of Zaria from Okene is 300°. The reverse bearing of Okene from Zaria is __________.
a) 120°
b) 60°
c) 480°

7. The bearing of X from Y is 270°. The bearing of Y from X is __________.
a) 90°
b) 0°
c) 180°

8. A true bearing of 315° represents a direction that is __________.
a) Southwest
b) Southeast
c) Northwest

9. The bearing of Lagos from Abuja is 120°. The reverse bearing of Abuja from Lagos is __________.
a) 120°
b) 240°
c) 300°

10. Magnetic bearings are influenced by the __________.
a) True north pole
b) Earth’s magnetic field
c) Equator

Please note that these questions are multiple-choice, and the correct answers are as follows:
1) c) North
2) c) Magnetic north pole
3) c) Due east
4) c) 0°
5) b) 135°
6) b) 60°
7) a) 90°
8) a) Southwest
9) b) 240°
10) b) Earth’s magnetic field

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Lesson Plan Presentation

Title: Understanding Bearings

Objective:
By the end of this lesson, students will be able to:
– Define bearings and understand their significance in navigation.
– Differentiate between true bearings and magnetic bearings.
– Determine the reverse bearing given a specific bearing.

Materials:
– Whiteboard or blackboard
– Markers or chalk
– Compasses
– Visual aids (diagrams, illustrations, or slides)
– Worksheets with practice problems
– Answer key for worksheets

Introduction (5 minutes):
1. Greet the students and engage them in a brief discussion about directions and navigation.
2. Ask the students if they have heard of the term “bearings” and what they think it means.
3. Introduce the topic by explaining that bearings are angles used to describe directions and help us navigate.

Main Body:

I. Definition and Significance of Bearings (10 minutes)
a. Explain that bearings are used to describe the direction of one point or object in relation to another.
b. Discuss the importance of bearings in navigation, cartography, and surveying.
c. Provide examples of real-life situations where bearings are used, such as finding directions on a map or using a compass.

II. True Bearings (15 minutes)
a. Define true bearings as angles measured with respect to the geographic north pole (true north).
b. Explain that the reference direction for true bearings is the north direction, assigned a bearing of 0 degrees.
c. Show visual aids or diagrams to help students visualize true bearings.
d. Demonstrate how to represent true bearings using three digits (tens, units, and minutes).
e. Give examples and ask students to practice converting directions into true bearings and vice versa.

III. Magnetic Bearings (15 minutes)
a. Define magnetic bearings as angles measured with respect to the magnetic north pole.
b. Explain that magnetic bearings are influenced by the Earth’s magnetic field and are read using a compass.
c. Discuss the difference between true north and magnetic north.
d. Show students how to determine magnetic bearings using compasses.
e. Provide examples and ask students to practice converting directions into magnetic bearings and vice versa.

IV. Reverse Bearings (10 minutes)
a. Explain that reverse bearings are used to find the opposite or reverse direction.
b. Demonstrate how to obtain the reverse bearing by adding or subtracting 180 degrees from the given bearing.
c. Give examples and ask students to practice finding reverse bearings.

Conclusion (5 minutes):
1. Summarize the key points discussed during the lesson.
2. Encourage students to practice using bearings in everyday life, such as giving directions or reading maps.
3. Address any questions or concerns the students may have.
4. Assign practice problems from the worksheet for homework.

Assessment:
– Monitor students’ participation and engagement during class discussions and activities.
– Review and grade the completed worksheets to assess students’ understanding of bearings and their ability to determine reverse bearings.

Note: Adapt the lesson plan duration based on the available class time and the students’ pace of learning.

Remember to provide ample opportunities for students to practice bearings through activities, discussions, and real-life examples. It’s important to create a supportive and interactive learning environment, allowing students to ask questions and actively participate in the lesson.

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