第 11 題
對我這種不懂輔助線的人而言,只好用代數硬做。
(借用 3 樓 老王老師的圖)
令 AD = BC = 1,CD = x,∠A = θ,則∠ACD = 30°- θ,,∠DBC = 90°- θ/2,由正弦定理:
x / sinθ = 1 / sin(30°- θ) ... (1)
x / cos(θ/2) = 1 / sin30° ... (2)
(2) / (1):
sinθ / cos(θ/2) = 2*sin(30°- θ)
sin(θ/2) = sin(30°- θ),又 0 < θ < 30°
θ/2 = 30°- θ
θ = 20°