📐 SAS 三角形计算器（两边夹角求全部）SAS Triangle Calculator (Two Sides and the Included Angle)

使用说明与常见问题How-to & FAQ

「SAS 三角形计算器（两边夹角求全部）」是什么？What is the SAS Triangle Calculator (Two Sides and the Included Angle) tool?

已知两边 a、b 及其夹角 C，用余弦定理求第三边 c，用正弦/余弦定理求另外两个角 A、B，并给出面积、周长、三条高、外接圆和内切圆半径，以及三角形类型（锐角/直角/钝角）。本地处理。Given two sides a and b and the included angle C, finds the third side c by the law of cosines and the other angles A and B, plus the area, perimeter, all three heights, circumradius, inradius and the triangle type (acute, right or obtuse). Processed locally.

如何使用「SAS 三角形计算器（两边夹角求全部）」？How do I use the SAS Triangle Calculator (Two Sides and the Included Angle) tool?

在「SAS 三角形计算器（两边夹角求全部）」中，填写「边 a」、「边 b」、「夹角 C°」等参数，结果会随输入实时计算并显示在下方。In the SAS Triangle Calculator (Two Sides and the Included Angle): Fill in "Side a", "Side b", "Angle C°"; results are recalculated instantly as you type.

SAS 是什么意思？What does SAS mean?

边-角-边：已知两条边和它们之间的夹角。这三个量唯一确定一个三角形。Side-angle-side: two sides and the angle between them, which fix the triangle uniquely.

第三边怎么求？How is the third side found?

用余弦定理 c² = a² + b² − 2ab·cos C。例如 a = 5、b = 6、C = 60°，c = √(25 + 36 − 30) = √31 ≈ 5.568。Use the law of cosines c² = a² + b² − 2ab·cos C. With a = 5, b = 6 and C = 60°, c = √(25 + 36 − 30) = √31 ≈ 5.568.

面积怎么算？How is the area found?

面积 = ½·a·b·sin C。上例面积 = ½ × 5 × 6 × sin 60° ≈ 12.99。Area = ½·a·b·sin C, so the example has area ½ × 5 × 6 × sin 60° ≈ 12.99.

能举个计算实例吗？Can you show a worked example?

例如在「SAS 三角形计算器（两边夹角求全部）」中填 边 a = 5，边 b = 6，夹角 C° = 60，结果区显示：边 c：5.567764；面积：12.990381；角 A：51.0517°；角 B：68.9483°；周长：16.567764；高 hₐ / h_b / h_c：5.196152 / 4.330127 / 4.666283；外接圆半径 R：3.21455；内切圆半径 r：1.568151；类型：锐角三角形；公式：c² = a² + b² − 2ab·cos CFor example, entering Side a = 5, Side b = 6, Angle C° = 60 in the SAS Triangle Calculator (Two Sides and the Included Angle) gives: Side c: 5.567764; Area: 12.990381; Angle A: 51.0517°; Angle B: 68.9483°; Perimeter: 16.567764; Heights hₐ / h_b / h_c: 5.196152 / 4.330127 / 4.666283; Circumradius R: 3.21455; Inradius r: 1.568151; Type: acute triangle; Formula: c² = a² + b² − 2ab·cos C

哪些输入会被检查？Which inputs are validated?

「SAS 三角形计算器（两边夹角求全部）」会检查这些输入——「边 a」、「边 b」：必须填写，须大于 0；「夹角 C°」：必须填写；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 SAS Triangle Calculator (Two Sides and the Included Angle) checks its inputs — "Side a", "Side b": required, must be greater than 0; "Angle C°": required; 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?

「SAS 三角形计算器（两边夹角求全部）」的设置：「边 a」默认 5；「边 b」默认 6；「夹角 C°」默认 60。每次生成结果都按当前设置处理。Settings in the SAS Triangle Calculator (Two Sides and the Included Angle) — "Side a" default 5; "Side b" default 6; "Angle C°" default 60. The result always uses the current settings.

计算精度如何？How precise are the results?

「SAS 三角形计算器（两边夹角求全部）」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 SAS Triangle Calculator (Two Sides and the Included Angle) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「SAS 三角形计算器（两边夹角求全部）」免费吗？需要注册吗？Is the SAS Triangle Calculator (Two Sides and the Included Angle) free? Do I need an account?

「SAS 三角形计算器（两边夹角求全部）」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 SAS Triangle Calculator (Two Sides and the Included Angle) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.