Pythagoras’ Theorem and Trigonometric Ratios | 勾股定理与三角函数

📚 Pythagoras’ Theorem and Trigonometric Ratios | 勾股定理与三角函数

In IGCSE Mathematics, right-angled triangles form the basis of two essential topics: Pythagoras’ theorem and trigonometric ratios. Pythagoras’ theorem connects the three side lengths of a right triangle, while sine, cosine and tangent connect side lengths to acute angles. These tools are used to find missing lengths, missing angles, and to solve practical problems in navigation, construction and 3D geometry.

在 IGCSE 数学中，直角三角形是两大核心主题的基础：勾股定理与三角函数。勾股定理建立了直角三角形三条边之间的关系，而正弦、余弦和正切则把边长与锐角联系起来。这些工具可用于求缺失的边长、缺失的角，以及解决航海、建筑和三维几何中的实际问题。

1. Identifying Right-Angled Triangles | 识别直角三角形

A right-angled triangle has one interior angle equal to 90°, and the side opposite this angle is always the longest side, called the hypotenuse. The other two sides are usually labelled as the adjacent and opposite sides relative to a chosen acute angle. Before applying Pythagoras or trigonometry, always confirm that the triangle is right-angled. In diagrams, a small square at a vertex marks the right angle.

直角三角形有一个内角等于 90°，与这个角

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