Question

A 1.6m tall girl stands at distance of 3.2m from a lamp post and casts shadow of 4.8m on the ground, then what is the height of the lamp post on ground, then what is the height of the lamp post

Answer 1

Answer is attached below

Answer 2

Answer:

The height of the lamp post is 2.64 meters.

Step-by-step explanation:

We are given that,

Height of the girl = 1.6 meters

Distance of girl from the lamp post = 3.2 meters

Distance of girl from the shadow = 4.8 meters

From the figure,we will find the angle θ using trigonometric form of the angles,

$\tan \theta=\frac{Perpendicular}{Base}$

i.e. $\tan \theta=\frac{1.6}{4.8}$

i.e. $\tan \theta=0.33$

i.e. $\theta=\arc tan 0.33$

i.e. θ = 18.26°

The height of the lamp post is given by,

$\tan \theta=\frac{Perpendicular}{Base}$

i.e. $\tan 18.26=\frac{x}{3.2+4.8}$

i.e. $\tan 18.26=\frac{x}{8}$

i.e. $x=8\times \tan 18.26$

i.e. $x=8\times 0.33$

i.e. x = 2.64 meters.

Thus, the height of the lamp post is 2.64 meters.