SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 95 of 100

Marks: +1, -0

The angles of depression of two ships from the top of a light house are 60° and 45° towards east. If the ships are 300 metre apart, the height of the light house is

200 $( 3 +√ { 3 } )$ meter
250 $( 3 +√ { 3 } )$ meter
150 $( 3 +√ { 3 } )$ meter
160 $( 3 +√ { 3 } )$ meter

Validate

Solution:

(3)

AB = Lamp post = h metre
C and D = Positions of ships
CD = 300 metre; BC = x metre
∠ACB = 60 metre; ∠ADB = 45°
In ΔABC,

\tan 60 °= { { AB } }/ { { BC } }

⇒√{ 3 } = { h }/ { x }

⇒h = √ { 3 } x

In ΔABD,

\tan 45°= { { AB } }/ { { BD } }

⇒ 1 = { h }/ { x + 300 }

⇒ h = x + 300

⇒ h = { h } /{ √{ 3 } } + 300

⇒ h - { h } /{ √ { 3 } } = 300

⇒ { √{ 3 } h - h } /{ √ { 3 } } = 300

⇒ h ( √{ 3 } - 1 ) = 300√ { 3 }

⇒ h = { 300 ( √{ 3 } ) } /{ √ { 3 } - 1 }

= { 300 √{ 3 } ( √ { 3 } + 1 ) }/ { ( √ { 3 } - 1 ) (√{ 3 } + 1 ) }

= { 300 ( 3 + √ { 3 } ) } /{ 2 }

= 150 ( 3 +√ { 3 } )

meter

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