研究了如下具有几何意义的三角不定方程(采用角度制)$$\frac{\sin (x^{\circ })\sin (y^{\circ })\sin (z^{\circ })}{\sin (A^{\circ }-x^{\circ })\sin (B^{\circ }-y^{\circ })\sin (C^{\circ }-z^{\circ })}=1,$$
其中$A,B,C$是给定的正整数,满足$2\le A\le B\le C$且$A+B+C=180$;\ $1\le x\le A-1,1\le y\le B-1,1\le z\le C-1$.设计了两种求解方案, 使用计算机按两种求解方案完整的求出了上述方程的所有正整数解.

This paper studies the following trigonometric indeterminate equation with geometric significance~(using degree measure) $$\frac{\sin (x^{\circ })\sin (y^{\circ })\sin (z^{\circ })}{\sin (A^{\circ }-x^{\circ })\sin (B^{\circ }-y^{\circ })\sin (C^{\circ }-z^{\circ })}=1,$$ where $A,B,C$ are given positive integers satisfying $2\le A\le B\le C,A+B+C=180$,\ $1\le x\le A-1,1\le y\le B-1,1\le z\le C-1$. Two methods to the above equation are formulated. Following these two methods,
all positive integer solutions of the equation are obtained via computer.