SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 94 of 100

Marks: +1, -0

The angle of elevation of an aeroplane as observed from a point 30 metre above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is

60 metre
45 metre
50 metre
75 metre

Validate

Solution:

(1)

AB = transparent water-surface
∠CPM = 30°; ∠C’PM = 60°
CM = h
CB = h + 30
∴ C’B = h + 30
In ΔCMP,

\tan 30° = { { CM } }/ { { PM } }

⇒ { 1 } /{ √ { 3 } } = { h }/ { { PM } }

⇒ { PM } = √{ 3 } h..... (i)

In ΔPMC’

\tan 60° = { { C' } { M } } /{ { PM } }

⇒√{ 3 } = { h + 30 + 30 }/ { { PM } }

⇒ { PM } = { h + 60 } /{ √{ 3 } }..... (ii)

∴√ { 3 } h = { h + 60 }/ {√ { 3 } }

⇒ 3h = h + 60

⇒ 2h = 60 ⇒ h = 30

∴ CB = BM + CM = 30 + 30= 60

metre

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