If the altitude of the sun is at 60∘, then the height of the vertical tower that will cast a shadow of length 30 m is ____.

If the altitude of the sun is at

60^{\circ}

, then the height of the vertical tower that will cast a shadow of length

30 m

30 \sqrt{3} m

.
Given that the altitude of the sun is at

60^{0}

and length of shadow of tower is 30 m.

Length of a shadow

BC = 30 m,

Angle of elevation at the top of the tower,

∠ ACB = 60^{\circ}

Let, the height of the tower

AB

h

Δ ABC

\Rightarrow \tan 60^{\circ} = \frac{AB}{BC}

\Rightarrow \tan 60^{\circ} = \frac{h}{30}

\Rightarrow \sqrt{3} = \frac{h}{30}

(

\tan 60^{\circ} = \sqrt{3}

)

\Rightarrow h = 30 \sqrt{3}

We know that,

AB = h

\Rightarrow AB = 30 \sqrt{3}

Therefore, the height of the vertical tower is

30 \sqrt{3} m

If the altitude of the sun is at $60^{\circ}$ , then the height of the vertical tower that will cast a shadow of length $30 m$ is ____.