Question

A ladder is placed in a slanting position against a wall such that it touches it 20 m above the ground. The foot of the ladder is 15 m away from the bottom of the building. What is the length of the ladder?

Answer 1

Hint: We can solve this using the Pythagoras theorem. Pythagora's theorem can be applied in right angled triangles. If we place a ladder against a wall, the ladder will form the hypotenuse, the wall will form the height and the ground will form the base. The wall and the ground make an angle of \[90{}^\circ \]. In this problem, we need to find the length of the ladder, that is, hypotenuse using the Pythagoras theorem.

Complete step-by-step answer:
First, we should make a diagram for better understanding. Since the ladder touches the wall 20 m above the ground, height will be 20 m. Also, the foot of the ladder is 15 m away, base will be 15 m. A diagram can be illustrated as follows:
     

To find the length of the ladder, we need to find AC.
According, to Pythagoras theorem,
\[\text{Hypotenus}{{\text{e}}^{2}}=\text{Heigh}{{\text{t}}^{2}}\text{ + Bas}{{\text{e}}^{2}}\]
Therefore, length of hypotenuse calculated as:
\[\text{A}{{\text{C}}^{2}}=\text{A}{{\text{B}}^{2}}+\text{B}{{\text{C}}^{2}} \]
\[ \text{A}{{\text{C}}^{2}}={{20}^{2}}+{{15}^{2}} \]
\[ \text{A}{{\text{C}}^{2}}=400+225 \]
\[ \text{A}{{\text{C}}^{2}}=625 \]
\[ \text{AC}=\sqrt{625} \]
\[ \text{AC}=25 \]
Therefore, the length of the ladder is 25 m.

Note: It is important that we make a correct diagram. We should mark the right angle at the correct place. If the angle between ladder and wall or between the ladder and ground is marked as \[90{}^\circ \], the length of ladder will be calculated incorrectly.