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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.
Solution
Let AB be a tower
CD be a stick, CD = 6m
Shadow of AB is BE = 28m
Shadow of CD is DF = 4m
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 Δ ABE ~ 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.
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