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ICSE Class X Math 2013 Paper

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In the figure given, from the top of a building AB=60 mA B = 60\,\mathrm{m} high, the angles of depression of the top and bottom of a vertical lamp post CDC D are observed to be 30∘30^{\circ} and 60∘60^{\circ} respectively. Find :
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Question : 31 of 46
Marks: +1, -0
The height of the lamp post.
Solution:  
Let AE=xAE=x and proved above BC=20BC=20 3 m\sqrt{3}\,\text{m}
∴    BC=ED=203\therefore \;\; BC=ED=20\sqrt{3}
Now in △\triangle AED,
tan⁡30∘  =  AEED\tan 30^{\circ}\;=\;\frac{AE}{ED}
⇒    13  =  AE203\Rightarrow\;\;\frac{1}{\sqrt{3}}\;=\;\frac{AE}{20\sqrt{3}}
⇒3AE  =203\Rightarrow \sqrt{3} AE\;=20\sqrt{3}
   now     AE  =20 m\;\text{ now }\;\; AE\;=20\,\text{m}
∴  EB  =AB−AE\therefore \; EB\;= AB - AE
∵  EB  =60−20=40 m\because \; EB\;=60-20=40\,\text{m}
∴  EB  =CD\therefore \; EB\;= CD
  CD  =40 m\; CD\;=40\,\text{m}
Hence, the height of the lamp post = 40 m40\,\text{m} .
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