📚 Bearings and Scale Drawings | 方位角与比例图
Bearings and scale drawings are essential tools for describing direction and representing real-world distances accurately. In the Cambridge KS3 mathematics course, students learn how to measure and draw bearings, how to use back bearings, and how to interpret and construct scale drawings. These skills link directly to Checkpoint exam questions on navigation, maps and geometric diagrams.
方位角和比例图是准确描述方向和表示实际距离的基本工具。在剑桥 KS3 数学课程中，学生学习如何测量和绘制方位角、如何使用反向方位角，以及如何解读和构建比例图。这些技能与 Checkpoint 考试中关于航海、地图和几何图形的题目直接相关。
1. What Is a Bearing? | 什么是方位角？
In navigation and geometry, a bearing is a way of describing the direction of one point from another. It is always measured clockwise from the north direction. For example, if a ship is exactly east of a lighthouse, the bearing of the ship from the lighthouse is 090°.
在航海和几何中，方位角是描述一个点相对于另一个点的方向的方法。它总是从正北方向顺时针测量。例如，如果一艘船在灯塔的正东方，那么从灯塔看这艘船的方位角是 090°。
Bearings are written using three digits, so 90° is written as 090°. This avoids confusion between directions such as 90° and 9°. The north direction itself has a bearing of 000°, east is 090°, south is 180°, and west is 270°.
方位角用三位数字表示，因此 90° 要写成 090°。这可以避免 90° 和 9° 等方向之间的混淆。正北方向的方位角是 000°，正东是 090°，正南是 180°，正西是 270°。
2. The Three-Figure Bearing Rule | 三位数方位角规则
A bearing must always be given as a three-digit angle. Angles smaller than 100° need extra zeros at the front. For example, a direction of 35° clockwise from north is written as 035°, and a direction of 8° is written as 008°.
方位角必须始终以三位数角度表示。小于 100° 的角度需要在前面补零。例如，从北顺时针 35° 的方向写为 035°，而 8° 的方向写为 008°。
Bearings are measured from the north line, not from the vertical line on the diagram or from any other line. The protractor must be placed with its centre at the starting point and its 0° mark pointing north.
方位角是从北线开始测量的，而不是从图中的竖直线或其他任何线开始。量角器的中心必须放在起点上，并且其 0° 刻度指向北方。
3. Measuring Bearings with a Protractor | 用量角器测量方位角
To measure the bearing of point B from point A, draw a light north line through A. Place the centre of the protractor at A and line up 0° with the north line. Then read the angle clockwise from north to the line AB. If the angle is greater than 180°, you may need to use a full-circle protractor or subtract from 360°.
要测量点 B 从点 A 出发的方位角，先通过 A 画一条淡淡的北向线。将量角器的中心放在 A 点，并将 0° 刻度与北向线对齐。然后从北顺时针读取到直线 AB 的角度。如果角度大于 180°，你可能需要使用全圆量角器，或者用 360° 减去较小的角。
tractor shows the smaller angle to the west is 60°, then the bearing is 360° - 60° = 300°.
例如，如果直线 AB 位于西北方向，从北顺时针测量的角可能在 270° 到 360° 之间。如果量角器显示偏西的较小角为 60°，那么方位角就是 360° - 60° = 300°。
4. Drawing a Bearing from a Point | 从一点绘制方位角
To draw a bearing, start by marking the point and drawing a clear north line upwards. Place the protractor so that its centre is on the point and 0° points north. Mark off the required angle clockwise from north. Finally, draw a straight line from the point through the mark and label it with the bearing.
要绘制方位角，首先标记起点并向上画一条清晰的北向线。将量角器的中心放在该点上，并使 0° 指向北方。从北顺时针标出所需的角度。最后，从该点经过标记画一条直线，并标出方位角。
In exam questions, you often have to draw a bearing such as 125° from a harbour H. A 125° bearing lies between east and south, closer to southeast. Accuracy is important: use a sharp pencil and check that the protractor has not moved while marking the angle.
在考试题中，你经常需要从港口 H 绘制如 125° 的方位角。125° 的方向位于正东和正南之间，更接近东南方向。准确性很重要：使用削尖的铅笔，并在标记角度时检查量角器是否移动。
5. Back Bearings and Their Calculation |
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