A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of $ 60^{\circ} $ with the wall, find the height of the wall.

Given:

A ladder 15 metres long just reaches the top of a vertical wall.

The ladder makes an angle of \( 60^{\circ} \) with the wall.

To do:

We have to find the height of the wall.

Solution:  

Let $AB$ be the wall and $AC$ be the length of the ladder.

From the figure,

$\mathrm{AC}=15 \mathrm{~m}, \angle \mathrm{BAC}=60^{\circ}$

Let the height of the wall be $\mathrm{AB}=h \mathrm{~m}$

We know that,

$\cos \theta=\frac{\text { Adjacent }}{\text { Hypotenuse }}$

$=\frac{\text { AB }}{AC}$

$\Rightarrow \cos 60^{\circ}=\frac{h}{15}$

$\Rightarrow \frac{1}{2}=\frac{h}{15}$

$\Rightarrow h=\frac{15}{2} \mathrm{~m}$

$\Rightarrow h=7.5 \mathrm{~m}$

Therefore, the height of the wall is $7.5 \mathrm{~m}$.     

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Updated on: 10-Oct-2022

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