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A vertical stick which is 15 cm long cas...

A vertical stick which is 15 cm long casts a 12-cm long shadow on the ground. At the same time, a vertical tower casts a 50-m-long shadow on the ground. Find the height of the tower.

Text Solution

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Let AB be the vertical stick and let AC be its shadow.
Then, `AB=0.15m and AC=0.12cm`
Let DE be the vertical tower and let DF be its shadow.
Then, DF=50 m. Let DE= xm.
Now, in `Delta BAC and Delta EDF`,
We have,
`angle BAC= angle EDF= 90^(@)`
`angle ACB= angle DEF` [ angular elevation of the sun at the same time]
`:. Delta BAC~ Delta EDF`
`rArr (AB)/(DE)=(AC)/(DF) rArr (0.15)/(x)=(0.12)/(50)`
`rArr x=((0.15xx50))/(0.12)=62.5`
Hence, the height of the tower is 62.2m
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