Question

A 1.2 m tall boy stands at a distance of 2.4 m from a lamppost and casts a shadow of 3.6 m on the ground. Find the height of the lamppost.

Answer 1

Solution:-
Let xy be the height of the lamppost and this is denoted by h meters.
Suppose ED be the height of the boy and DZ be the length of the shadow of the boy.
Given: ED = 1.2 m (height of boy), XD = 2.4 m (distance from the lamppost) and DZ = 3.6 m (length of the shadow).
In triangle EDZ,
tan Z = ED/DZ  (tan theta = perpendicular/base)
tan Z = 1.2/3.6 = 1/3  ...(1)
In triangle YXZ,
tan Z = XY/XZ
tan Z = h/(2.4+3.6)
⇒ 1/3 = h/(2.4+3.6)  [Using (1),Since tan Z = 1/3]
⇒1/3 = h/6
⇒ 3h = 6
⇒ h = 2 m
The height of the lamppost is 2 m.

Answer 2

Height of Lamp post is 2 m