Question

A fireman's ladder, 100m long reaches a point on the highrise building that is 80 m above of the ground. lf the ground is horizontal, how many meters from the fot of the building is the foot of the ladder?​

Answer 1

Diagram :-

$\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(0,0){\line(0,3){2.65cm}}\put(-4,5){\sf\footnotesize 80m}\put(0,0){\line(3,0){2cm}}\put(10,0){\line(-3,4){2cm}}\put(6,6){\sf\footnotesize 100m}\put(2,-2){\sf\footnotesize land = ?}\end{picture}$

Solution :-

By the given information ,

• The wall forms a right angle with the land
• Height of wall = 80m
• Length of ladder = 100m

We need to find ,

• Distance between the wall & Ladder ( base of ∆ )

Now , finding the base of ∆ using Pythagoras theorem.

Hypotenuse² = Base² + Height²

Here ,

• Hypotenuse = length of ladder = 100m
• Base = Distance between wall & ladder = ?
• Height = wall = 80m

Substituting we have ,

$\implies \sf 100^2 = \rm Base^2 + \sf 80^2$

$\sf\implies 10000 = \rm Base^2 + \sf 6400$

$\sf\implies 10000 - 6400 = \rm Base^2$

$\sf\implies 3600 = \rm Base^2$

$\rm\implies Base = \sqrt{\sf 3600}$

$\implies \underline{\boxed{\textbf{\textsf{Base = 60m}}}}$

Hence , distance between the ladder & foot of wall = 60m

Answer 2

Diagram :

$\setlength{\unitlength}{1.5 cm}\begin{picture}(0,0)\linethickness{0.7mm}\qbezier(1, 0)(1,0)( 1,3)\qbezier(5,0)(5, 0)(1,3)\qbezier(5,0)(1,0)(1,0)\put(1.4,0){\line(0,3){0.3}}\put(1,0.3){\line(1,0){0.4}}\put(-0.1,1.5){80 m}\put(0.5,-0.2){ \sf B }\put(3.1,2){100 m}\put(2.9, - 0.4){Land = ?}\put(5.1, - 0.2){ \sf C }\put(0.6, 2.9){ \sf A }\end{picture}$

Answer:

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,

$=> \sf AC^2 = AB^2 + BC^2$

$=> \sf (100)^2 = (80)^2 + BC^2$

$=> \sf 10000= 6400 + BC^2$

$=> \sf BC^2 = 10000 - 6400$

$=> \sf BC^2 = 3600$

Taking square roots on both sides we get :]

$=> \sf BC = \sqrt{3600 }$

$=> \textsf{ \textbf{ BC= 60 meters}}$

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