(10分) 如图，Rt△ABC中，∠C = 90°，把Rt△ABC绕着B点逆时针旋转，得到Rt△DBE，点E在AB上．（1）若∠BDA = 70°，求∠BAC的

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(10分) 如图，Rt△ABC中，∠C = 90°，把Rt△ABC绕着B点逆时针旋转，得到Rt△DBE，点E在AB上．

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

答案

（1）∠BAC =
（2）

解析

解：(1) 由旋转得△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，
设AD边上的高为h
∴
∴······················································· 10分