Question

(8分) 現有一張寬為12cm練習紙，相鄰兩條格線間的距離均為0.8cm．調皮的小聰在紙的左上角用印章印出一個矩形卡通圖案，圖案的頂點恰好在四條格線上（如圖），測得∠α＝32°．

1.（1）求矩形圖案的面積；

2.（2）若小聰在第一個圖案的右邊以同樣的方式繼續蓋印（如圖），最多能印幾個完整的圖案？

（參考數據：sin32°≈0.5，cos32°≈0.8，tan32°≈0.6）

 

Answer 1

【答案】

 

1.（1）如圖，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

∴橡皮的長和寬分別為2cm和1.6cm．

                                                                       

 

 

 

 

 

 

 

 

2.（2）如圖，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，∴最多能擺放5塊橡皮．···················· 8分

 

【解析】略