📐 钝角三角形判定器（锐角/直角/钝角）Obtuse Triangle Checker (Acute / Right / Obtuse)
由三边用余弦定理判定锐角、直角或钝角：比较最大边平方与另两边平方和。须满足三角不等式。本地处理。Classify acute, right or obtuse from three sides via the cosine rule: compare the largest side squared with the sum of the other squares. Must satisfy the triangle inequality. Processed locally.
使用说明与常见问题How-to & FAQ
「钝角三角形判定器（锐角/直角/钝角）」是什么？What is the Obtuse Triangle Checker (Acute / Right / Obtuse) tool?
由三边用余弦定理判定锐角、直角或钝角：比较最大边平方与另两边平方和。须满足三角不等式。本地处理。Classify acute, right or obtuse from three sides via the cosine rule: compare the largest side squared with the sum of the other squares. Must satisfy the triangle inequality. Processed locally.
如何使用「钝角三角形判定器（锐角/直角/钝角）」？How do I use the Obtuse Triangle Checker (Acute / Right / Obtuse) tool?
在「钝角三角形判定器（锐角/直角/钝角）」中，填写「边 a」、「边 b」、「边 c」等参数，结果会随输入实时计算并显示在下方。In the Obtuse Triangle Checker (Acute / Right / Obtuse): Fill in "Side a", "Side b", "Side c"; results are recalculated instantly as you type.
只判定类型，算面积吗？Does it also find the area?
本页只判定锐角/直角/钝角。面积可用海伦公式或其他三角形工具。This page only classifies acute/right/obtuse. Use Heron or another triangle tool for area.
边的顺序有影响吗？Does side order matter?
没有。会自动取最长边当作斜边/对角边来比较。No. The longest side is taken automatically for the comparison.
能举个计算实例吗？Can you show a worked example?
例如在「钝角三角形判定器（锐角/直角/钝角）」中填 边 a = 3，边 b = 4，边 c = 6，结果区显示：类型：钝角；最大边² 与 另两边² 和之差：11For example, entering Side a = 3, Side b = 4, Side c = 6 in the Obtuse Triangle Checker (Acute / Right / Obtuse) gives: Type: Obtuse; c² − (a²+b²): 11
哪些输入会被检查？Which inputs are validated?
「钝角三角形判定器（锐角/直角/钝角）」会检查这些输入——「边 a」：必须填写，须大于 0且不大于 1,000,000,000,000,000；「边 b」：必须填写，须大于 0且不大于 1,000,000,000,000,000；「边 c」：必须填写，须大于 0且不大于 1,000,000,000,000,000；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Obtuse Triangle Checker (Acute / Right / Obtuse) checks its inputs — "Side a": required, must be more than 0 and at most 1,000,000,000,000,000; "Side b": required, must be more than 0 and at most 1,000,000,000,000,000; "Side c": required, must be more than 0 and at most 1,000,000,000,000,000; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「钝角三角形判定器（锐角/直角/钝角）」的设置：「边 a」默认 3；「边 b」默认 4；「边 c」默认 6。每次生成结果都按当前设置处理。Settings in the Obtuse Triangle Checker (Acute / Right / Obtuse) — "Side a" default 3; "Side b" default 4; "Side c" default 6. The result always uses the current settings.
计算精度如何？How precise are the results?
「钝角三角形判定器（锐角/直角/钝角）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Obtuse Triangle Checker (Acute / Right / Obtuse) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「钝角三角形判定器（锐角/直角/钝角）」免费吗？需要注册吗？Is the Obtuse Triangle Checker (Acute / Right / Obtuse) free? Do I need an account?
「钝角三角形判定器（锐角/直角/钝角）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Obtuse Triangle Checker (Acute / Right / Obtuse) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.