Question

A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Answer 1

Let AB be a tower

CD be a stick, CD = 6 m

Shadow of AB is BE = 28 m

Shadow of CD is DF = 4 m

At same time light rays from sun will fall on tower and stick at same angle.

So, ∠DCF = ∠BAE

And ∠DFC = ∠BEA

∠CDF = ∠ABE (Tower and stick are vertical to ground)

Therefore ΔABE ~ ΔCDF (By AA similarity)

So,

`"AB"/"CD"="BE"/"DF"`

`"AB"/6=28/4`

`"AB"=28xx6/4=42` m

So, height of tower will be 42 metres.