Question

A ladder is placed in such a way that its foot is at a distance of 5 m from a wall and its tip reaches a window 12 m above the ground. Determine the length of the ladder.
(a) 13 m
(b) 112 m
(c) 11 m
(d) 15 m

Answer 1

Hint: To solve the given problem, it is important to draw the diagram according to the given conditions and understand the problem. After the diagram, use the Pythagoras theorem, to find the length of the ladder.

Complete step by step answer:
Here, we have been given that the foot of the ladder is at a distance of 5 m from the wall and the tip of the ladder is at 12 m where there is a window. Therefore, let us find the length of the ladder given.
First, let us draw the diagram to better understand the given conditions.

The above diagram represents the ladder, the wall, and the distance of the foot of the ladder from the wall. Let us consider that the window is at point A, the foot of the ladder is at point C, B is a point where the wall is perpendicular to the ground. Therefore, we got a triangle ABC as a right-angled triangle.
Since it is a right-angled triangle, we can use the Pythagoras theorem, to find the length of the ladder. Let us consider the length of the ladder also the hypotenuse of the triangle ABC as $x$.
We know,
According to Pythagoras theorem,
\[{{\left( \text{Hypotenuse} \right)}^{2}}={{\left( \text{side one} \right)}^{2}}+{{\left( \text{side two} \right)}^{2}}\]
                    $\begin{align}
  & {{\left( x \right)}^{2}}={{\left( 12 \right)}^{2}}+{{\left( 5 \right)}^{2}} \\
 & =144+25 \\
 & =169
\end{align}$
Now, let us take square root on both the sides, we get
$\begin{align}
  & \sqrt{{{x}^{2}}}=\sqrt{169} \\
 & \sqrt{x\times x}=\sqrt{13\times 13} \\
 & x=13
\end{align}$
Hence, the length of the ladder is 13 m.

Note:
 In this question, we considered the wall is perpendicular to the ground because it is common sense if the wall is not perpendicular to the ground, there is a chance of wall collapsing. Hence, whenever the wall is built it is to be taken as perpendicular to the ground. There is another way to find the length of th ladder, consider the angle between the foot of the ladder and the ground as $\theta $ and find the angle and use $\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}}$ to find the angle$\left( \theta \right)$. Then, use $\sin \theta =\dfrac{\text{Opposite}}{\text{Hypotenuse}}$ to find the length of the ladder.