The shadow of a lamp is $3\sqrt{3}$ m long when the angle of elevation of the sun is 60°. Arushi is of height 3 m standing in front on the lamp post.

(i) What is the height of the lamp post?

(ii) What is the length of shadow of Aarushi ?

(iii) How far is Aarushi from the lamp post ?

Given,

Shadow of lamp post = $3\sqrt{3}$ m

Angle of elevation of sun = 60°

Height of Aarushi = 3 m

(i) tan 60° = $\dfrac{\text{Height of lamp post}}{\text{Length of shadow of lamp post}}$

We know that :

tan 60° = $\sqrt{3}$

$\sqrt{3} = \dfrac{h}{3\sqrt{3}}$

h = $3\sqrt{3} × \sqrt{3}$ = 3 × 3 = 9 m.

Hence, height of lamp post = 9 m.

(ii) Length of shadow of Aarushi,

tan 60° = $\dfrac{\text{Height of Arushi}}{\text{Length of shadow of Arushi}}$

$\sqrt{3} = \dfrac{3}{\text{}}$

Length of shadow of Arushi = $\dfrac{3}{\sqrt{3}} = \sqrt{3}$ m.

Hence, length of shadow of Aarushi = $\sqrt{3}$ m.

(iii) From figure :

Distance of Aarushi from lamp post = Length of shadow of lamp post - Length of shadow of Aarushi

Distance = $3\sqrt{3} - \sqrt{3} = 2\sqrt{3}$ m.

Hence, distance of Aarushi from lamp post = $2\sqrt{3}$ m.