~F.2 Maths(Long question X1)

1. In the figure, a ladder AB 2.6 m long is placed against a vertical wall, and the foot of the ladder is 1 m away from the wall. If the top of the ladder slides downwards by 0.4m, how far will the foot of the ladder slide? (Give your answer correct to 2 decimal places.)

圖片參考：http://hk.geocities.com/namsm4e/p0103.jpg

如圖可見若梯的頂部向下移 0.4m，則梯腳離牆為 (1 + x)m，
則可用畢氏定理
2.62 = 2.22 + (1 + x)2
(1 + x)2 = 1.92
1 – x = 1.39m
所以
x = 0.39m

2007-04-06 11:14:37 補充：
對起計錯數應先求梯頂離地的高度y = √(2.6^2 - 1.0^2) = 2.4m所以梯頂下降 0.4m，變成離地 2.4 – 0.4 = 2m後再求2.6^2 = 2.0^2 + (1 + x)^2(1 + x)^2 = 2.761 + x = 1.66mx = 0.66m

Let the length from the top of the ladder to the ground be ACm,
AC^2 + CB^2 = AB^2
AC^2 +1^2=2.62
AC^2=5.76
AC=2.4
After the top of the ladder downwards by 0. 4m,
The foot of the ladder is x m from the wall,
(2.4-0.4)^2 + x^2 = 2.62
2^2 + x^2 = 6.76
x^2 = 2.76
X = 1.66 (2 decimal places.)