A person walking along a straight road towards a hill observ es at two points with distance \sqrt3 km. between them the angles of elevation of the hill to be 30° and 60°. What is the height of the hill?

TS ICET 23 May 2018 Shift 1 Paper

Question : 121 of 200

Marks: +1, -0

A person walking along a straight road towards a hill observ es at two points with distance

√3

km. between them the angles of elevation of the hill to be 30° and 60°. What is the height of the hill?

$√3 /2$ km
$1/2$ km
1 km
$3/2$ km

Validate

Solution:

Let AB represent the hill of height h.
Let C and D be the points from which the angles of elevation to top of hill are 600 and 300 respectively.
Let BC = x
In ΔABC,

\tan60°=h/x⇒x=h/√3

→ (1)
In ΔABD,

\tan30°=h/{x+√3}⇒x+√3=h√3

→ (2)

From (1) and (2)

h/√3+√3=h√3⇒h=3/2

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