MathematicsThe length of shadow of a tower on the plane ground is √3 times the height of the tower. Find the angle of elevation of sun.

The length of shadow of a tower on the plane ground is √3 times the height of the tower. Find the angle of elevation of sun.

Given,
The length of the shadow of a tower on the plane ground is

\sqrt{3}

times the height of the tower.
Let the height of the tower be AB.
The length of the shadow of a tower

BC = \sqrt{3}

AB
Let angle of elevation of the Sun be

θ

ΔABC

tanθ = \frac{perpendicular}{Base}

\Rightarrow tanθ = \frac{AB}{BC}

\Rightarrow tanθ = \frac{AB}{\sqrt{3} AB}

\Rightarrow tanθ = \frac{1}{\sqrt{3}}

We know that

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

\Rightarrow θ = 30^{\circ}

Therefore,the angle of elevation of the Sun is

30^{\circ}

.
Hence, option 2 is correct.

JEE