# Bearings

## Overview

Overview:

In General Mathematics, the topic of Bearings delves into the precise way of expressing direction or location of one point in relation to another. Bearings are essential in navigation, surveying, and various real-life applications that require accurate orientation information. The concept of bearings involves understanding angles in a compass direction starting from the north direction and rotating clockwise.

One of the primary objectives of studying bearings is to comprehend the concept of angles of elevation and depression. Angles of elevation are the angles formed above the horizontal line when looking up at an object, while angles of depression are the angles formed below the horizontal line when looking down at an object. These angles play a crucial role in determining the bearing of one point from another accurately.

Calculating distances and angles using bearings is another key aspect covered in this topic. By applying trigonometric ratios of sine, cosine, and tangent of angles, students learn how to determine distances between points and angles with precision. Tables of trigonometric ratios, especially for standard angles like 30 degrees, 45 degrees, and 60 degrees, are instrumental in these calculations.

Moreover, the utilization of sine and cosine rules aid in solving complex problems related to bearings. These rules allow for finding missing sides or angles in triangles when the information provided is limited. Graphs of trigonometric ratios further enhance the understanding of how these ratios behave across different angles, facilitating visual interpretation and problem-solving skills.

Real-life applications of bearings extend to scenarios like determining the height of objects or structures, calculating distances between points in maps or landscapes, and establishing the direction of one point relative to another. Whether it is calculating the bearing of an aircraft, locating a hidden treasure based on given bearings, or surveying lands accurately, the knowledge of bearings and trigonometry is indispensable.

By mastering the concept of bearings and its applications, students not only enhance their mathematical skills but also develop a practical understanding of how mathematics is intricately intertwined with everyday navigation and spatial orientation. The ability to interpret bearings, calculate distances, and angles using trigonometric principles equips individuals with essential problem-solving tools that can be applied in diverse scenarios.

## Objectives

1. Solve real-life problems involving bearings
2. Apply trigonometric ratios in bearings problems
3. Understand the concept of bearings
4. Calculate distances and angles using bearings
5. Determine bearings of one point from another

## Lesson Note

Bearings are a way of describing the direction one point is from another using angles. They are commonly used in navigation to find the direction from one place to another. Understanding bearings is crucial in solving real-life problems related to distance and direction.

## Lesson Evaluation

Congratulations on completing the lesson on Bearings. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. Find the bearing of point B from point A if A is located at coordinates (2,4) and B is located at coordinates (6,8). A. N45°E B. S45°W C. S45°E D. N45°W Answer: A. N45°E
2. Find the distance between points P(3, 5) and Q(9, 3). A. 2 units B. 6 units C. 8 units D. 10 units Answer: C. 8 units
3. If the bearing of X from Y is N30°E, what is the bearing of Y from X? A. S60°W B. S30°W C. N60°W D. N30°W Answer: D. N30°W
4. Point A is 10 km directly north of point B. What is the bearing of point B from point A? A. S90°E B. S90°W C. N90°W D. N90°E Answer: B. S90°W
5. A tree is located at a bearing of N40°E from a point P, and a tower is located at a bearing of S50°E from the same point P. What is the difference in the angle between the tree and the tower? A. 10° B. 90° C. 100° D. 140° Answer: A. 10°
6. Given that the bearing of Y from X is N60°W, what is the bearing of X from Y? A. S30°E B. S60°E C. N30°E D. N60°E Answer: D. N60°E
7. If the bearing of a ship from a lighthouse is N45°E and the lighthouse is directly north of the ship, what is the direction of the ship from the lighthouse? A. East B. West C. North D. South Answer: A. East
8. A plane is flying on a bearing of N60°E. If the wind is blowing towards N, what is the true bearing of the plane's direction? A. N60°E B. N60°W C. S30°E D. S30°W Answer: D. S30°W
9. Given that the bearing of point R from point Q is S50°W and the bearing of point S from Q is N40°E, what is the difference in the bearings of R and S from Q? A. 10° B. 50° C. 90° D. 180° Answer: A. 10°
10. If the bearing of point T from point U is S40°E and the bearing of point V from U is N60°W, what is the bearing of V from T? A. N20°W B. S80°W C. N20°E D. S80°E Answer: D. S80°E

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Bearings from previous years

Question 1

If x is a real number which of the following is more illustrated on the number line?

Question 1

A ship sails 6km from a port on a bearing 070° and then 8km on a bearing of 040°. Find the distance from the port.

Practice a number of Bearings past questions