A ladder leaning against the wall makes an angle of $60^{o}$ with the horizontal. if the foot of the ladder is $3\ m$ away from the wall. find the length of the ladder.

Given: A ladder leaning against the wall makes an angle of $60^{o}$ with the horizontal and the foot of the ladder is $3\ m$ away from the wall. 

To do: To find the length of the ladder.

Solution:

Let $AC$ be a ladder, $AB$ is the wall and $BC$ is the ground as shown in the figure.

$BC=3\ m,\ \angle ACB=60^o$

$cos60^o=\frac{BC}{AC}$

$\Rightarrow \frac{1}{2}=\frac{3}{AC}$

$\Rightarrow AC=6\ m$

Thus, the length of the ladder is $6\ m$.

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Updated on: 10-Oct-2022

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