a maths

I got the totally different answer from yours.

Since the length of the ladder is 12.5m
and the height 6.4m.

|
| -> the wall 6.4m
|
|___________________________
x

x = the maximum value of the horizontal disace that the ladder extends beyong the wall.

the diagram is actually a triangle.(I couldn't draw the ladder with slashes, what i can do is to only write the number to represent the ladder.)

use the Pythagorean theorem

12.5^2 -6.4^2 = sqrt (156.25 - 40.96)= sqrt (115.29) = 10.73m

so the answer should be 10.73m

Let angle between the wall and the ladder be t.
Since height of wall = 6.4m, so length of ladder from top of wall to the ground
= 6.4/cos t.
So length of ladder extended beyond the wall = 12.5 - 6.4/cos t.
Since the horizontal distance that the ladder extends beyond the wall = x,
therefore, x = (12.5 - 6.4/cos t)sin t = 12.5sin t - 6.4tan t.
dx/dt = 12.5 cos t - 6.4/cos^2(t).
Put dx/dt = 0, we get
12.5cos t = 6.4/cos^2(t)
cos^3(t) = 6.4/12.5
cos t = cube root of 0.512 = 0.8
So tan t = 3/4.
So max. of x = 12.5(0.8) - 6.4(0.75) = 10 - 4.8 = 5.2m.