三角函数基础
Trigonometry basics
在直角三角形中利用正弦、余弦和正切（sin、cos、tan）求出未知边和未知角，包括根据题目条件写出正确的三角比。
Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem
学习证据 / Evidence
- 根据已知边和未知边，判断应使用哪个三角比（正弦=对边/斜边，余弦=邻边/斜边，正切=对边/邻边）。
- 已知一个角和一条边，用正弦、余弦或正切求出未知边的长度。
- 利用反三角函数（如 tan⁻¹）求出未知角。
- Identify which trigonometric ratio to use (SOH CAH TOA) based on the known and unknown sides
- Calculate an unknown side using sin, cos, or tan and a known angle
- Find an unknown angle using the inverse trigonometric function (e.g. tan⁻¹)
评估问题 / Assessment
如果{{name}}知道一架梯子长5米，靠在墙上并与地面成70°角，那么{{name}}能否用三角函数算出梯子顶端离地面的高度？
If {{name}} knows a ladder is 5 metres long and leans against a wall at 70° to the ground, can they use trigonometry to work out how high up the wall it reaches?