Question

A ladder, 100m long reaches a point on the high-rise building that is 80m

above the ground. If the ground is horizontal, how many meters from the foot
of the building is the foot of the ladder?

Answer 1

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,

`AC^2 = AB^2 + BC^2`

`100^2 = 80^2 + BC^2\\\\10000 = 6400 + BC^2\\\\BC^2 = 10000 - 6400\\\\BC^2 = 3600`

Taking square root on both sides,

`BC = √(3600)\\\\BC = 60`

Thus the distance between the foot of building to foot of ladder is 60 meters