Question

A man 1.8m high stands at a distance of 3.6m from a lamp post and cast its shadow of 5.4m on the ground. Find the height of the lamp post.

Answer 1

Let the Height of the man be H and Height of Lamp post be H"

According to Question  H = 1.8 m

Let distance between Man and Lamp post be x = 3.6 m
Distance of Shadow = y = 5.4 m

Let Angle made by the Man and the Lamp post at Distance (x+y) be Theta

According to the angle of the triangle formed,

For man, tan theta = H / y = 1.8 / 5.4 = 1/3                            

For lamp post,   tan theta = H' / (x+y) = H' / (5.4+3.6) = H' / 9 

equating above equations, 
                          H' / 9 = 1/3
                          H' = 9 / 3 = 3 m
Thus height of lamp post is 3 m

Answer 2

$\huge\sf\green{Answer:-}$

• Let "H" be height.

• Height = 1.8 m.

• Let "x" be the distance between Man and Lamp post be = 3.6 m.

• ( y = 5.4 ) m is the distance of Shadow.

Hence :

$\sf = > Distance = (x+y). (Theta) \\ </p><p>\sf = > tan \: \: theta = \frac{h}{y} = \frac{1.8}{5.4} = \frac{1}{3} \: ->(Man) \\ \sf = > tan \: \: theta = \frac{h}{(x + y) } = \frac{h}{5.4 + 3.6} = \frac{h}{9} \: ->(lamp \: post)$

Calculation:

$\sf => \frac{h}{9} = \frac{1}{3} \\ </p><p>\sf => h = \frac{9}{3} = 3 m$

3 m = height of lamp post.