Question

A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a tower casts a shadow 30 m long. Determine the height of the tower

Answer 1

Length of stick = 10cm 

Length of shadow stick= 8cm 

Length of shadow of tower = hcm

In ΔABC and ΔPQR

∠B = ∠C = 90º   And ∠C = ∠R (angular elevation of sum)

Then ΔABC ~ ΔPQR (by AA similarty)

So, \(\frac{AB}{PQ}\) = \(\frac{BC}{QR}\)

Or\(\frac{10 cm}{8 cm}\) = \(\frac{H}{3000}\)

Or h= \(\frac{10}{8}\) x 3000

Or 3750 cm 

Or 37.5 m