trig. solution

來源: 於 2024-05-31 14:05:59 [舊帖] [給我悄悄話] 本文已被閱讀：次

AB=DC=a, AD=b:

sinx/AD = sin(54-x)/DC => sinx/b = sin(54-x)/a, or  a/b=sin(54-x)/sinx

from triangle ABD,  AB/AD=sin54/sin84 => a/b=sin54/sin84

so: sin(54-x)/sinx=sin54/sin84, or   sin84sin54cosx - sin84cos54sinx = sin54sinx

=> tanx = sin84sin54/(sin54+sin84cos54), with calculator   x = 30°

but, so far no clue how to get it from geometric method.