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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Updated on: 10-Oct-2022

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