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Question
A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is
Options
100 m
120 m
25 m
200 m
Solution
Given: Vertical stick 20m long casts a shadow 10m long on the ground. At the same time a tower casts the shadow 50 m long on the ground.
To determine: Height of the tower
Let AB be the vertical stick and AC be its shadow. Also, let DE be the vertical tower and DF be its shadow.
Join BC and EF.
In ΔABC and ΔDEF, we have
`∠A=∠D=90^o`
`∠C=∠F`
`Δ ABC ∼ Δ DEF`
We know that in any two similar triangles, the corresponding sides are proportional. Hence,
`(AB)/(DE)=(AC)/(DF)`
`20/(DE)=10/50`
`DE=100m`
Hence the correct answer is option `a`.
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