Bearings and Scale Drawings | 方位角与比例绘图

📚 Bearings and Scale Drawings | 方位角与比例绘图

Bearings and scale drawings are essential tools in mathematics for describing direction and representing real-world distances on paper. In the Cambridge KS3 curriculum, you need to measure, draw and interpret bearings, and use scale factors to convert between diagram lengths and actual lengths.

方位角和比例绘图是数学中用于描述方向和将实际距离表示在纸上的重要工具。在剑桥 KS3 课程中，你需要测量、绘制和解释方位角，并会使用比例尺在图示长度与实际长度之间进行转换。

1. Understanding Bearings | 理解方位角

A bearing is a way of describing direction. It is always measured from the north line in a clockwise direction. For example, a bearing of 090° means due east, 180° means due south, 270° means due west and 000° means due north.

方位角是一种描述方向的方式。它总是从北线开始按顺时针方向测量。例如，方位角 090° 表示正东，180° 表示正南，270° 表示正西，000° 表示正北。

Bearings are used by ships, aircraft and walkers because they give an exact direction that does not depend on the way a person is facing. A bearing is normally written using three digits, such as 045°, even if the angle is less than 100°.

方位角被船只、飞机和徒步者使用，因为它给出的精确方向不会随人面朝的方向而改变。方位角通常写作三位数字，例如 045°，即使角度小于 100°。

2. Three Key Rules for Bearings | 方位角的三条关键规则

Rule 1: Always measure from the north line. The starting line must point vertically upwards on the diagram.

规则一：始终从北线开始测量。起始线在图上必须垂直向上。

Rule 2: Always measure clockwise. If a point is to the east, the bearing is 090°, not 270°.

规则二：始终按顺时针方向测量。如果一个点在东方，方位角是 090°，而不是 270°。

Rule 3: Always write bearings with three digits. Use leading zeros when needed, for example 008° or 075°.

规则三：方位角始终写成三位数字。在需要时使用前导零，例如 008° 或 075°。

You should memorise these cardinal and intercardinal bearings because they appear in many questions.

你应该记住这些基本方位角，因为它们在许多题目中都会出现。

3. Measuring Bearings from a Diagram | 从图中测量方位角

To measure the bearing of point B from point A, first draw a north line at A. Then connect A to B with a straight line. Place your protractor with its centre at A and 0° pointing north. Read the angle clockwise from the north line to the line AB.

要测量从点 A 到点 B 的方位角，先在点 A 处画一条北线。然后用直线连接 A 和 B。将量角器的中心放在 A 点，0° 指向北方。从北线顺时针读取到直线 AB 的角度。

If the angle is greater than 180°, you may need to measure the smaller angle and subtract it from 360°. For example, if the line points north-west, the bearing might be 315°, which is 360° – 45°.

如果角度大于 180°，你可能需要先测量较小的角，再用 360° 减去它。例如，如果直线指向西北方向，方位角可能是 315°，也就是 360° – 45°。

Always double-check that your answer is between 000° and 360°. A bearing can never be negative or greater than 360°.

始终检查答案是否在 000° 到 360° 之间。方位角不可能为负，也不可能大于 360°。

4. Drawing a Bearing from a Point | 从一点绘制方位角

To draw a bearing, start by marking the point clearly. Draw a vertical north line upwards from the point. Place the protractor with its centre on the point and 0° aligned with the north line. Make a small mark at the required bearing, then remove the protractor and draw a straight line from the point through the mark.

要绘制一个方位角，先清楚地标出该点。从该点向上画一条垂直北线。将量角器的中心对准该点，0° 对准北线。在所需方位角处做一个小记号，然后移开量角器，从该点经过记号画一条直线。

For example, to draw a bearing of 120°, measure 120° clockwise from north and mark that position. The line should point to the south-east.

例如，要绘制方位角

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

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