Question

A 1.5 m tall boy stands at a distance of 3m from a lamp post and cast a shadow of 4.5 m on the ground. Find the height of the lamp post .

Answer 1

Let the height of the lamp post be AB = h m  

Let the height of boy be CD = 1.6m 

Let the shadow of boy be DE = (BD produced) = 4.5m  

In a triangle CDE, tan theta = 1.5/4.5 = 1/3 --- (1) 

In a triangle ABE, tan theta = h/7.5  [BE =BD + DE = 3 + 4.5 = 7m ] --- (2) 

If we equate 1 and 2  

1/3 = h/7.5 

H = 7.5/3  = 5/2 

So the height of lamp post is 5/2m