Question

(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．

 

Answer 1

【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