Question

The ladder is inclined to the top of the $12.3$ m high wall. Which of the following is length of the pole?

• A. $4.1$ m
• B. $3.01$ m
• C. $12.3$ m
• D. Cannot be determined

Answer 1

The correct option is A $4.1$ m

The above situation can be shown as,

naming the points this diagram can be shown as,

In triangles $△ABC$ and $△DEB$
$\angle ABC=\angle DEB\left({90}^o\right)$
$\angle ACB=\angle DBE$ (given)
So,$△ABC$~$△DEB$ (AA property)

$\Rightarrow \frac{BE}{CB}=\frac{DE}{AB}\text{(corresponding sides of similar triangles are in same ratio)}$

As, $\frac{BE}{BC}=\frac{1}{3}$ (given)
So,
$\frac{DE}{AB}=\frac{1}{3}$
$DE=\frac{1}{3}\times AB$
$DE=\frac{1}{3}\times 12.3$
$DE=4.1$ m
Hence, option$\left(a\right)$ correct.