A 1.6 m talk girl stands at a distance of 3.2 m from a lamp post and cast a shadow of 4.8 m on the ground , then the height of the lamp post is
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Answer:
Using trigonometric ratios.
Let AB be the height of lamp post.
Now, in right △CDE,
⇒tanθ=
DC
ED
=
4.8
1.6
=
3
1
⟶(1)
In , △ACB,
⇒tanθ=
BC
AB
=
3.2+4.8
AB
=
8
AB
⟶(2)
From (1)&(2) we get
⇒
3
1
=
8
AB
⇒AB=
3
8
=2.67m
∴ Height of the lamp post =2.67m
(ii) Using similar triangles :
In △CDE&△CBA
i)∠CDE=∠CBA=90°
ii)∠DCE=∠BCA (Common)
∴△CDE∼△CBA ( By AA similarities )
Hence,
AB
DE
=
BC
CD
⇒AB=
CD
DE×BC
=
4.8
1.6×8
=
3
8
=2.67m
∴ Height of lamp post =2.67m.
Hence, the answer is 2.67.
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