Mastering Pythagoras’ Theorem and Right-Angled Trigonometry | 精通勾股定理与直角三角形三角学

📚 Mastering Pythagoras’ Theorem and Right-Angled Trigonometry | 精通勾股定理与直角三角形三角学

For IGCSE Mathematics, Pythagoras’ Theorem and right-angled trigonometry are among the most frequently tested topics. They appear in both Paper 2 and Paper 4, often hidden inside word problems, bearings, and three-dimensional geometry questions. This guide covers every core skill you need: the theorem itself, Pythagorean triples, the three trigonometric ratios, exact values, angles of elevation and depression, and a reliable step-by-step problem-solving strategy.

在 IGCSE 数学中，勾股定理与直角三角形三角学是考查频率最高的内容之一。它们频繁出现在 Paper 2 和 Paper 4 中，常隐藏于应用题、方位角以及三维几何问题里。本指南将系统梳理你所需的全部核心技能：勾股定理本身、勾股数、三大三角函数比值、特殊角精确值、仰角与俯角，以及一套可靠的逐步解题策略。

1. The Pythagorean Theorem | 勾股定理

The Pythagorean theorem applies only to right-angled triangles. It relates the two shorter sides, a and b, to the longest side, c, known as the hypotenuse. The hypotenuse is always opposite the 90° angle and is always the longest side.

勾股定理仅适用于直角三角形。它描述了直角边 a、b 与最长边 c（即斜边）之间的关系。斜边始终在 90° 角的对边，且永远是最长边。

c² = a² + b²

To find the hypotenuse, use c = √(a² + b²). To find a shorter side, rearrange the formula: a = √(c² − b²) or b = √(c² − a²).

求斜边时使用 c = √(a² + b²)；求直角边时需变形：a = √(c² − b²) 或 b = √(c² − a²

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

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