📚 The Sine Rule | 正弦定理
The sine rule is a fundamental identity in triangle trigonometry. It links each side of a triangle to the sine of its opposite angle, allowing you to find missing sides or angles in non-right-angled triangles. For Edexcel A-Level Mathematics, you must be able to use it confidently, understand the ambiguous case, and choose between the sine rule and cosine rule.
正弦定理是三角学中的一个基本恒等式。它将三角形的每条边与对角的正弦联系起来，使你能在非直角三角形中求缺失的边或角。对于 Edexcel A-Level 数学，你必须能熟练运用它、理解歧义情形，并能在正弦定理与余弦定理之间做出正确选择。
1. What the Sine Rule Says | 正弦定理的内容
For any triangle ABC, label side a opposite angle A, side b opposite angle B, and side c opposite angle C. The sine rule states:
对于任意三角形 ABC，将边 a 标记为角 A 的对边，边 b 标记为角 B 的对边，边 c 标记为角 C 的对边。正弦定理指出：
a / sin A = b / sin B = c / sin C
The reciprocal form is equally valid:
其倒数形式同样成立：
sin A / a = sin B / b = sin C / c
Some versions also write the common ratio as 2R, where R is the radius of the circumcircle, but the core exam requirement is the equality of the three ratios.
有些版本还会把公共比值写成 2R，其中 R 是外接圆半径，但考试的核心要求是三个比值相等。
2. When to Use the Sine Rule | 何时使用正弦定理
Use the sine rule when you know:
在以下情况下使用正弦定理：
- two angles and one side (AAS or ASA);
- two sides and a non
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