SSC CPO SI and ASI 2011 Paper

Question : 145 of 200

Marks: +1, -0

If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metre. The height of the pillar is

Solution:

(4)

Let height of the pillar PQ be h m and length of shadow QR be a m.
Therefore, QS will be (a – 20) m.
In ΔPQS,

\tan 45^{\°}=\ {\ {PQ}}/{\ {QS}}=\ {\ {h}}/{\ {a}-20} \⇒ \ {a}=\ {h}+20

Δ{PQR}

\tan 30^{\°}=\ {\ {PQ}}/{ {QR}} \⇒ {1}/{\√{3}}

= { {h}}/{ {a}} ⇒{h}+20=√{3} {h}

Hence,

\ {h}=\ {20}/{\√{3}-1} ×{\√{3}+1}/{\√{3}+1}=10(\√{3}+1) {m}

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