AS / GS

(a).
Let ∠A0A1A2=x,
x=∠A0A1A2=∠A1A2A3=∠A2A3A4...(alt.∠s of // lines)
cosx=9/10
cos∠A1A2A3=cosx=(A2A3)/9
cos∠A2A3A4=cosx=(A3A4)/(A2A3)
cos∠A3A4A5=cosx=(A4A5)/(A3A4)
cos∠A4A5A6=cosx=(A5A6)/(A4A5)

A2A3=9cosx=9(9/10)=81/100
A3A4=(A2A3)cosx=(81/100)(9/10)=729/1000
A4A5=(A3A4)cosx=(729/1000)(9/10)=6561/10000
A5A6=(A4A5)cosx=(6561/10000)(9/10)=59049/100000

(b)
From (a),
A0A1=10=10(9/10)^0
A1A2=9=10(9/10)^1
A2A3=81/10=10(9/10)^2
A3A4=729/100=10(9/10)^3
A4A5=6561/1000=10(9/10)^4
...
A_[n] A_[n+1]=10(9/10)^n

Sum of A0A1+A1A2+...A_[n] A_[n+1] is
http://s1099.photobucket.com/albums/g395/jasoncube/?action=view¤t=568bb8b7.jpg



圖片參考：http://imgcld.yimg.com/8/n/HA00016323/o/701109110065113873456570.jpg


So, the answer is 10.