SSC CPO SI and ASI 2016 Paper

Question : 121 of 200

Marks: +1, -0

From the top and bottom of a straight hill, the angles of depression and elevation to the top of a pillar of height 10 m are observed to be 60° and 30°, respectively. The height (in metres) of the hill is

Validate

Solution:

(3) Let AB be the hill and EC be the pillar as shown below.

\ln \Δ{CBE}

\tan 30°= { {CE}}/{ {CB}} ⇒{1}/{\√{3}}= {10}/{ {x}}

⇒x=10√{3} {m}

\Δ {FAE}

\tan 60°= { {AD}}/{\ {x}} ⇒ √{3}= { {AD}}/{ {x}}

⇒ A D=10√{3} ×√{3}=30 {m}

Hence, height of the hill = AD + DB = 30 + 10 = 40 m.

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