Question

A $5.5\text{m}$ long ladder is leaned against a wall . The ladder reaches the wall to a height of $4.4\text{m}$ . Find the distance between the wall and the foot of ladder.

Answer 1

Find the distance between the wall and foot of the ladder : Here we find the distance $\text{PQ}$

If we see the given figure then we find that it is a right angle triangle . So we will use the PYTHAGORAS THEOREM , to find the distance .

$\text{RP=4.4 m ,RQ=5.5 m, PQ = ?}$

Here $\text{RQ}$ is the hypotenuse and $\text{RP}$ is the perpendicular and $\text{PQ}$ is the base of the given triangle .

Pythagoras Theorem : ${\text{H}}^2{\text{=B}}^2{\text{+P}}^2$

$$\begin{gathered} {\text{RQ}}^2{\text{=PQ}}^2{\text{+RQ}}^2 \\ {\text{(5.5)}}^2{\text{=PQ}}^2{\text{+(4.4)}}^2 \\ {\text{(5.5)}}^2{\text{-(4.4)}}^2{\text{=PQ}}^2 \\ {\text{30.25-19.36=PQ}}^2 \\ {\text{PQ}}^2\text{=10.89} \\ \text{PQ=}\sqrt{10.89}\text{=3.3 m} \end{gathered}$$

Hence the distance $\text{PQ}$ is $3.3\text{m}$.