If the ratio of the height of a tower and the length of its shadow is

Question:

If the ratio of the height of a tower and the length of its shadow is $\sqrt{3}: 1$, what is the angle of elevation of the Sun?

Solution:

Let  be the angle of elevation of sun is.

Given that: Height of tower is  meters and length of shadow is 1.

Here we have to find angle of elevation of sun.

In a triangle,

$\Rightarrow \tan \theta=\frac{A B}{B C}$

$\Rightarrow \tan \theta=\frac{\sqrt{3}}{1}\left[\because \tan 60^{\circ}=\sqrt{3}\right]$

$\Rightarrow \tan \theta=\sqrt{3}$

$\Rightarrow \theta=60^{\circ}$

Hence the angle of elevation of sun is $60^{\circ} .$

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