Q13 of 25 Page 9

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.

To find:


The height of lamp post.


Formula Used:



Explanation:



(i) 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


=


=


=


In ∆ABO


=


=



Therefore, height of lamp post is


(ii) By Similar of triangles property


In ∆ABO and in ∆CDO


∠ABO = ∠CDO = 90°


∠AOB = ∠COD


∆ABO ∆CDO (AA similarity)


For similar ∆s sides are in ratio


Hence,



=



Therefore height of lamp post is 8/( 3 ) m.


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