Question

(10分) 如圖，Rt△ABC中，∠C = 90°，把Rt△ABC繞著B點(diǎn)逆時(shí)針旋轉(zhuǎn)，得到Rt△DBE，點(diǎn)E在AB上．

（1）若∠BDA = 70°，求∠BAC的度數(shù)．
（2）若BC = 8，AC = 6，求△ABD中AD邊上的高．

Answer 1

（1）∠BAC =
（2）

解：(1) 由旋轉(zhuǎn)得△ACB≌△DEB
∴BD = BA
∴∠BAD =∠BDA =
∴∠ABD =
∴∠ABC =∠ABD =
∵∠C =
∴∠BAC =·········································································· 5分
(2) ∵BC = 8，AC = 6，∠C =
∴
∵∠DEB =∠C =且BE = BC = 8，DE ="AC" = 6
∴AE =" AB" – BE = 2
在Rt△DEA中，
設(shè)AD邊上的高為h
∴
∴······················································· 10分