MathematicsThe ratio of the length of a rod and its shadow is 1:3. The angle of elevation of the sun is:

The ratio of the length of a rod and its shadow is $1 : \sqrt{3}$ . The angle of elevation of the sun is:

Given that the ratio of the length of a rod and its shadow is

1 : \sqrt{3}

Let

AB

be the rod and

AC

be its shadow.
Let us assume the angle of elevation

Δ ACB = α

AB : AC = 1 : \sqrt{3}

To find out the angle

α

\tan α = \frac{AB}{AC}

\Rightarrow \tan α = \frac{1 h}{h \sqrt{3}}

\Rightarrow \tan α = \frac{1}{\sqrt{3}}

\Rightarrow \tan α = \tan 30^{\circ}

[Since

\tan 30^{\circ} = \frac{1}{\sqrt{3}}

]

\Rightarrow α = 30^{\circ}

Therefore the angle of elevation of the sun is

30^{\circ}

.
Hence the correct option is 1.

JEE