The distance between the foot of building to foot of ladder is 60 meters
Solution:
Given that A ladder, 100 m long reaches a point on the high-rise building that is 80 m above the ground
Given that ground is horizontal
The ladder, building and ground forms a right angled triangle
The figure is attached below
In the right angled triangle ABC,
AC represents the length of ladder
AC = 100 m
AB represents the height of building
AB = 80 m
BC represents the distance between the foot of building to foot of ladder
BC = ?
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition for right angled triangle ABC,
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]100^2 = 80^2 + BC^2\\\\10000 = 6400 + BC^2\\\\BC^2 = 10000 - 6400\\\\BC^2 = 3600[/tex]
Taking square root on both sides,
[tex]BC = \sqrt{3600}\\\\BC = 60[/tex]
Thus the distance between the foot of building to foot of ladder is 60 meters
