三角形计算器 Triangle Calculator
根据已知边长与角度（如三边、两边及夹角、两角及一边）自动计算其他未知量，包括三边长度、三个角度、周长与面积。
Enter known sides and angles (e.g. SSS, SAS, ASA/AAS) and this tool will solve the triangle: unknown sides, angles, perimeter and area.
1. 输入条件 · Triangle Inputs
3. 计算方法小结 · How This Triangle Calculator Works
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三边已知（SSS）· Three sides known:
已知 a、b、c 三边时，先检查是否满足三角形不等式（任意两边之和大于第三边）。然后通过余弦定理：
When a, b, c are known, the triangle inequality is checked first (sum of any two sides > the third). Then the law of cosines is used to get the angles.
例如：cos A = (b² + c² − a²) / (2bc)，再通过 arccos 得到角 A。Angles B、C 类似计算。面积则用海伦公式。
Example: cos A = (b² + c² − a²) / (2bc), then A = arccos(…). Angles B and C are computed similarly. Area is computed with Heron’s formula. -
两边及夹角（SAS）· Two sides & included angle:
已知两边及夹角时，先使用余弦定理求第三边，再回代求出其余两个角。
With two sides and the included angle, the third side is found via the law of cosines, then the remaining angles are computed.
提示： 夹角必须是真正的“夹角”，即位于两条已知边之间的那个内角。
Tip: the included angle must truly lie between the two known sides. -
两角及一边（ASA/AAS）· Two angles & one side:
已知两角 A、B 以及对角边 a 时，先用 A + B + C = 180° 求出 C，再使用正弦定理：
Given angles A, B and their opposite side a, angle C is computed from A + B + C = 180°. Then the law of sines is used: a/sin A = b/sin B = c/sin C.
注意： 若 A + B ≥ 180°，则无法构成三角形，需要检查输入是否有误。
Note: if A + B ≥ 180°, the triangle is impossible; your inputs must be adjusted.
说明：本工具默认以角度（°）为单位进行三角函数计算，内部会自动在角度与弧度间转换。结果为理论值，未考虑测量误差与数值舍入对实际应用的影响。
仅用于学习与快速估算，不构成工程设计或精密测量依据。
Note: Angles are interpreted in degrees and converted to radians internally for trigonometric functions.
Results are theoretical and do not account for measurement errors or rounding in real-world applications.
Use this calculator for study and quick estimation only, not for precise engineering work.
