Question

A man of height 175 cm stands at a distance of 4 metres from a lamppost AB. If the lamp A is at a height of 5.25 m from the point B on the ground, what is the length of the man's shadow on the ground?

Answer 1

Answer:

Length of the man's shadow = 2m.

Step-by-step explanation:

Given :

Height of the man = 175 cm = 1.75 m.

Height of the lamp-post AB = 5.25 m.

Man's distance from the lamp-post = 4 m.

To find :

The man's shadow on the ground.

Solution :

Let A be the top point and B be the base point of lamp-post.

Let man is standing at point C and CD is the height of the man, i.e. CD = 1.75 m.

Let CS be the shadow of the man.

Now, the two ∆s ABS and DCS will be similar

{ by A-A similarity rule }

Therefore, AB/DC = BS/CS

=> 5.25/1.75 = (4 + x)/x

{ let CS = x, then BS = BC + CS = 4 + x }

=> 3 = (4 + x)/x

=> 3x = 4 + x

=> 2x = 4

=> x = 2

Hence, length of the shadow = 2 m.