Question

(8分) 现有一张宽为12cm练习纸，相邻两条格线间的距离均为0.8cm．调皮的小聪在纸的左上角用印章印出一个矩形卡通图案，图案的顶点恰好在四条格线上（如图），测得∠α＝32°．

1.（1）求矩形图案的面积；

2.（2）若小聪在第一个图案的右边以同样的方式继续盖印（如图），最多能印几个完整的图案？

（参考数据：sin32°≈0.5，cos32°≈0.8，tan32°≈0.6）

Answer

1.（1）如图，在Rt△BCE中，

∵sinα=，∴BC = = = 1.6··········································································· 2分

∵矩形ABCD中，∴∠BCD=90°，∴∠BCE+∠FCD=90°，

又∵在Rt△BCE中，∴∠EBC+∠BCE=90°，∴∠FCD=32°．

在Rt△FCD中，∵cos∠FCD=，∴CD===2··············································· 4分

∴橡皮的长和宽分别为2cm和1.6cm．

2.（2）如图，在Rt△ADH中，易求得∠DAH=32°．∵cos∠DAH=，

∴AH===2··································································································· 5分

在Rt△CGH中，∠GCH=32°．∵tan∠GCH=，

∴GH=CG tan32°= 0.8×0.6 = 0.48··················································································· 7分

又∵6×2+0.48＞12，5×2+0.48＜12，3×4+0.9616，∴最多能摆放5块橡皮．···················· 8分

【解析】略