美夢成真教甄討論區

[幾何]

cotC = -cot(A + B) = (1 - cotAcotB)/(cotA + cotB)
令 cotA = 3t，cotB = 5t，cotC = 27t
(1 - 15t^2)/(8t) = 27t
t = ± 1 / √231 (負不合)
cotA = 3 / √231，cotB = 5 / √231，cotC = 27 / √231

sinA = √385 / 20，sinB = √231 / 16，sinC = √385 / 40
AB：BC：CA = sinC：sinA：sinB = (√385 / 40)：(√385 / 20)：(√231 / 16) = 2：4：√15
令 AB = 2，BC = 4，CA = √15
BD = 1，CD = 3，AD = √15 / 2
剩下的就簡單了 ......