Question

A 1.6m tall, girl stands ata distance of 3.2m from a lamp-post and cats a shadow of 4.8m on the grond. Find the height of the lamp-post by using (i)trignometric ratios (ii)property of similiar triangles.

Answer 1

Let AB be the tower of height h m
Then CD to be the height of the girl &DE be the length of the shadow of the girl
If CD=1.6m,AD=3.2cm &DE=4.8m
In ΔCDE
tan E=CD/ED (tan∅ perpendicular/base)
tan E=1.6m/4.8m=1/8................(i)
in ΔBAE
tan E=AB/AE
Therefore 1/3=hm/(3.2+4.8)
1/3=h/8
h=8/3(length of the lamp)