题干

2013年9月23日强台风“天兔”登录深圳,伴随着就是狂风暴雨.梧桐山山坡上有一棵与水平面垂直的大树,台风过后,大树被刮倾斜后折断倒在山坡上,树的顶部恰好接触到坡面(如图所示).已知山坡的坡角∠AEF=23°,量得树干的倾斜角为∠BAC=38°,大树被折断部分和坡面所成的角∠ADC=60°,AD=3m.

(1)求∠DAC的度数;

(2)求这棵大树折断前的高度.(结果保留根号)

 

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答案(点此获取答案解析)

解:(1)延长BA交EF于一点G,如图所示,

则∠DAC=180°﹣∠BAC﹣∠GAE=180°﹣38

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