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 : 30 of 46

Marks: +1, -0

The horizontal distance between

A B

and

C D

Solution:

Given :

{\AB}=60 {\m}

\; ∵ \;\; ∠ P {\PAC}=60^{∘}

\; ∴ \;\; ∠ {\PAC}=∠ {\BCA}

Now in

△ {\ABC}

\tan 60^{∘}\;=\;{ {\AB}}/{ {\BC}}

{√{3}}\;=\;{60}/{ {\BC}}

⇒ \;\; {\BC}\;=\;{60}/{{√{3}}} × \;{{√{3}}}/{{√{3}}}

{\BC}\;=\;{60 {√{3}}}/{3}=20 {√{3}} {\m}

Hence, the horizontal distance between

{\AB}

and

{\CD}=20 {√{3}} {\m}

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