Question

The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder?

Answer 1

Hint:
We will draw the figure first of all to get a clear understanding of the question. We will use Pythagoras theorem to solve this question in the right angle triangle formed with the wall, ladder and the ground. The Pythagoras theorem states: In a right angled triangle, the square of the hypotenuse of the triangle is equal to the sum of squares of the other two sides (i.e., base and the perpendicular of the triangle).

Complete step by step solution:
We are given an arrangement where a ladder of length of 15 m is placed slanting to a wall and its top reaches a window which is 9 m high.
Let us draw the figure:

From the figure, we can see that ABC is a right angled triangle in which ladder AC is resting against the wall AB. B is the base of the wall and A is the position of the window.
Here, $\angle $ B = 90°. Therefore, using the Pythagoras theorem in triangle ABC, we get
$ \Rightarrow {\text{A}}{{\text{C}}^2} = {\text{A}}{{\text{B}}^2} + {\text{ B}}{{\text{C}}^2}$
$
   \Rightarrow {15^2} = {9^2} + {\text{B}}{{\text{C}}^2} \\
   \Rightarrow 225 - 81 = {\text{B}}{{\text{C}}^2} \\
   \Rightarrow 144 = {\text{B}}{{\text{C}}^2} \\
   \Rightarrow {\text{BC = }}\sqrt {144} = 12 \\
$

Therefore, the distance between the base of the wall and that of the ladder is found to be 12 m.

Note:
It is the direct application of Pythagoras theorem, However, it’s applications are vast and diverse. One variation of the given question is, instead of one side they would have given us one angle. In that case we can use trigonometric ratios to solve.