SSC CPO SI and ASI 2015 Paper

Question : 116 of 199

Marks: +1, -0

The two banks of a canal are straight and parallel. A, B, C are three persons, among whom, A stands on one bank and B and C on the opposite bank. B find that the angle ABC is 30°, and C finds that the angle ACB is 60°. If B and C are 100 metres apart, thebreadth of the canal is

$\ {25}/{\√ {3}}$ metres
20 $\ √{3}$ metres
25 $\√{3}$ metres
$\ {20}/{\√{3}}$ metres

Validate

Solution:

(3)

Let BD = p m then CD = (100 – p)m and let AD = q m
In

\tan 30^{\°}=\ {A D}/{B D} \⇒ \ {1}/{\√{3}}=\ {q}/{p} \⇒ p=\√{3} q

\ .......(i)

\Δ A C D,

\tan 60^{\°}=\ {A D}/{\ {CD}} \⇒ \√{3}= {q}/{100-\ {p}}

\⇒ 100 √{3}-\√{3} \ {p}=\ {q}

Therefore,

100 \√{3}-3 q=q . . . . .

(i)

⇒ q=25 \√{3} m

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