# Ex.6.5 Q9 Triangles Solution - NCERT Maths Class 10

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## Question

A ladder $$10$$$$\rm{}m$$ long reaches a window $$8$$$$\rm{}m$$ above the ground. Find the distance of the foot of the ladder from base of the wall.

Diagram

## Text Solution

Reasoning:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Steps:

$$AB$$ is height of the windows from the ground = $$8$$$$\rm{}m$$

$$AC$$ is the length of the ladder = $$10$$$$\rm{}m$$

$$BC$$ is the foot of the ladder from the base of ground $$= ?$$

Since $$\Delta ABC$$ is right angled triangle $$\,(\angle ABC={{90}^{0}})$$

\begin{align} \Rightarrow B C^{2} &=A C^{2}-A B^{2} \text { (Pythagoras theorem) } \\ B C^{2}&=10^{2}-8^{2} \\ B C^{2}&=100-64 \\ B C^{2} &=36 \\ B C &=6 \rm{}m \end{align}

The distance of the foot of the ladder from the base of the wall =$$6$$$$\rm{}m$$

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