Q. 213.9( 8 Votes )

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.

Answer :

Let the height of the lamp post = h (m)


And height of girl is CD = 1.6 m.


Length of shadow is OD = 4.8 m.


In ∆CDO


= ------(1)


In ∆ABO


=


=




By Smilariting


In ∆ABO and in ∆CDO


ABO = CDO = 90°



AOB = COD


∆ABO ∆CDO (AA similarity)


For similar ∆s sides are in ratio


Hance,



=




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