📚 Master Bearings and Scale Drawings | 掌握方位角与比例绘图
This revision guide covers the essential skills for solving Cambridge KS3 problems on bearings and scale drawings. You will learn how to measure, draw and check bearings, and how to use scale factors to convert diagram lengths into real distances.
本复习指南涵盖剑桥 KS3 数学中方位角与比例绘图的关键技能。你将学习如何测量、绘制和检查方位角，以及如何使用比例因子把图上长度换算成实际距离。
1. What Are Bearings? | 什么是方位角？
A bearing is a way of describing direction using angles. It is measured clockwise from the north line, which points straight up on a diagram. Bearings are used in navigation, map reading and construction.
方位角是一种用角度描述方向的方法。它从指北线（在图中竖直向上）按顺时针方向测量。方位角用于航海、地图阅读和建筑施工。
In everyday language we might say north-east or south-west, but a bearing gives a precise angle. For example, east is 090 degrees, south is 180 degrees and west is 270 degrees.
在日常语言中我们会说东北或西南，但方位角给出精确的角度。例如，东方是 090 度，南方是 180 度，西方是 270 度。
2. The Three Rules of Bearings | 方位角的三条规则
Cambridge questions expect you to follow three rules every time you state or draw a bearing.
剑桥试题要求你在每一次写出或绘制方位角时都遵守三条规则。
- Always measure from the north line.
- Always measure clockwise.
- Always write the bearing as a three-digit number, such as 035° or 215°.
- 始终从指北线开始测量。
- 始终按顺时针方向测量。
- 始终把方位角写成三位数，例如 035° 或 215°。
For example, an angle of 40° measured clockwise from north is written as 040°, not 40°. A bearing of 8° is written as 008°.
例如，从北顺时针测量 40° 的角应写成 040°，而不是 40°。方位角 8° 应写成 008°。
3. Measuring Bearings with a Protractor | 用量角器测量方位角
To measure the bearing from one point to another, place the centre of the protractor on the starting point. Align the 0° marking with the north line. Then read the angle clockwise until the line joining the two points is reached.
要测量从一点到另一点的方位角，把量角器的中心放在起点上。将 0° 刻度线与指北线对齐。然后按顺时针方向读取角度，直到到达连接两点的线段。
If the angle is less than 100°, always add leading zeroes to make three digits. Many protractors show both clockwise and anticlockwise scales, so make sure you read the correct scale from north.
如果角度小于 100°，一定要在前面补零成为三位数。许多量角器同时显示顺时针和逆时针刻度，因此务必从北线开始读取正确的刻度。
Bearing = Angle measured clockwise from north, written in three digits
方位角 = 从北顺时针测量的角度，写成三位数
4. Drawing Bearings Accurately | 准确绘制方位角
When a question asks you to draw a bearing, start by drawing a clear north line through the starting point. Place the protractor with its centre on the point and 0° pointing north.
当题目要求绘制方位角时，先在起点画一条清晰的指北线。把量角器的中心对准该点，0° 指向北方。
Mark a small dot at the required angle, for example 120°. Remove the protractor, join the starting point to the dot, and label the angle with the three-digit bearing.
在所需角度（例如 120°）处标记一个小圆点。移开量角器，把起点和圆点连接起来，并用三位数方位角标注这个角度。
For a complete journey diagram, you should draw each leg using the same scale. Keep north lines parallel at each new point; this is essential for measuring the next bearing correctly.
对于完整的行程图，你应该用相同的比例绘制每一段。每个新点处的指北线必须互相平行；这对于正确测量下一个方位角至关重要。
5. Back Bearings | 反向方位角
A back bearing is the bearing you would travel on to return from a point to the starting point. It is found by adding 180° to the original bearing if it is less than 180°, or subtracting 180° if it is 180° or more.
反向方位角是从某个点返回起点时所沿的方位角。如果原方位角小于 180°，就加上 180°；如果原方位角大于或等于 180°，就减去 180°。
- Bearing from A to B is 060°, so the back bearing from B to A is 240°.
- Bearing from A to B is 210°, so the back bearing from B to A is 030°.
- 从 A 到 B 的方位角是 060°，所以从 B 到 A 的反向方位角是 240
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