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Find the angle of elevation of the sun (sun's altitude) when the length of the shadow of a vertical pole is equal to its height.
Given:
The length of the shadow of a vertical pole is equal to its height.
To do:
We have to find the angle of elevation of the sun
Solution:
Let $AB$ be the pole and $AC$ be the shadow.
Let the height of the pole be $\mathrm{AB}=h \mathrm{~m}$ and the length of the shadow be $\mathrm{AC}=h \mathrm{~m}$.
Let the angle of elevation be $\theta$.
We know that,
$\tan \theta=\frac{\text { Opposite }}{\text { Adjacent }}$
$=\frac{\text { AB }}{AC}$
$\Rightarrow \tan \theta=\frac{h}{h}$
$\Rightarrow \tan \theta=1$
$\Rightarrow \tan \theta=\tan 45^{\circ}$
$\Rightarrow \theta=45^{\circ}$ [Since $\tan 45^{\circ}=1$]
Therefore, the angle of elevation is $45^{\circ}$.
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