ICSE Class X Math 2013 Solved Paper

In the figure given, from the top of a building $A B=60 {\m}$ high, the angles of depression of the top and bottom of a vertical lamp post $C D$ are observed to be $30^{∘}$ and $60^{∘}$ respectively. Find :

Question : 31 of 46

Marks: +1, -0

The height of the lamp post.

Solution:

Let

{\AE}=x

and proved above

{\BC}=20

{√{3}} {\m}

∴ \;\; {\BC}= {\ED}=20 {√{3}}

Now in

△

AED,

\tan 30^{∘}\;=\;{ {\AE}}/{ {\ED}}

⇒\;\;{1}/{{√{3}}}\;=\;{ {\AE}}/{20 {√{3}}}

⇒ {√{3}} {\AE}\;=20 {√{3}}

\;\text " now "\;\; {\AE}\;=20 {\m}

∴ \; {\EB}\;= {\AB}- {\AE}

∵ \; {\EB}\;=60-20=40 {\m}

∴ \; {\EB}\;= {\CD}

\; {\CD}\;=40 {\m}

Hence, the height of the lamp post =

40 {\m}

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