已知△ABC中,∠B=60°,∠C=45°,AC-AB=根号下6-2,求BC长,

Question

已知△ABC中,∠B=60°,∠C=45°,AC-AB=根号下6-2,求BC长,

Answer 1

过A做AM⊥BC
∵∠C=45° ∠B=60°
∴CM=ACsin45° =√2/2AC BM=ABsin60­=1/2AB
由勾股定理得
AM²=AC²-CM²=AC²-(√2/2AC)²=1/2AC²
AM²=AB²-BM²=AB²-(1/2AB)²=3/4AB²
∴1/2AC²=3/4AB²
AC=√6/2AB
∵AC-AB=√6-2
∴√6/2AB-AB=√6-2
(√6-2)/2AB=√6-2
AB=2
AC=√6
所以BC=CM+BM=√2/2×√6+1/2×2=√3+1