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Question
A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.
Solution
Let AC be the lamp post of height h
We assume that ED = 1.6 m, BE = 4.8 m and EC = 3.2 m
We have to find the height of the lamp post
Now we have to find the height of lamp post using similar triangles.
Since triangle BDE and triangle ABC are similar.
`(AC)/(BC) = (ED)/(BE)`
`h/(4.8 + 3.2) = 1.6/(BE)`
`h = 8/3`
Again, we have to find height of lamp post using trigonometric ratios.
In ΔADE
`=> tan theta = 1.6/4.8`
`=> tan theta = 1/3`
Again in ΔABC
`=> tan theta = h/(4.8 + 3.2)`
`=> 1/2 = h/8`
`h = 8/3`
Hence the height of lamp post is 8/3 m
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