設AC=X, AB=Y.
tan(a) = Y/(X+15) (由角平分線定理或直接作輔助線。) tan(2a) = Y/15, tan(3a) = Y/7. 代入正切的和角公式,得 Y^2 = 8X + 15. 代入X^2 = 15^2 + Y^2, 解得X=20.