The distance between the foot of building to foot of ladder is 60 meters
<em><u>Solution:</u></em>
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,
![AC^2 = AB^2 + BC^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%20AB%5E2%20%2B%20BC%5E2)
![100^2 = 80^2 + BC^2\\\\10000 = 6400 + BC^2\\\\BC^2 = 10000 - 6400\\\\BC^2 = 3600](https://tex.z-dn.net/?f=100%5E2%20%3D%2080%5E2%20%2B%20BC%5E2%5C%5C%5C%5C10000%20%3D%206400%20%2B%20BC%5E2%5C%5C%5C%5CBC%5E2%20%3D%2010000%20-%206400%5C%5C%5C%5CBC%5E2%20%3D%203600)
Taking square root on both sides,
![BC = \sqrt{3600}\\\\BC = 60](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B3600%7D%5C%5C%5C%5CBC%20%3D%2060)
Thus the distance between the foot of building to foot of ladder is 60 meters