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 = 6m 

Shadow of AB is BE = 28cm 

Shadow of CD is DF = 4m 

At same time light rays from sun will fail on tower and stick at the same angle

So,∠DCF = ∠BAE

And ∠DFC = ∠BEA

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

Therefore ΔABE ~ ΔCDF (By AAA similarity)

So, AB/CD = BE/DF 

AB/6 = 28/4 

AB/6 = 7 

AB = 7 x 6 

AB = 42 m 

So, height of tower will be 42 meter.