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UPSC CDS 2 2022 Math Paper

Consider the following for the next two (02) items that follow :

The angle of elevation of a cloud at

\mathrm{C}

from a point

(\mathrm{P}), \mathrm{H}

metres above the surface of a lake is

30^{\circ}

. The height of the cloud from the surface of the lake is

2\ \mathrm{H}

metres. Let

\theta

be the angle of depression of the reflection of the cloud in the lake from the point

P

Question : 56 of 100

Marks: +1, -0

What is the value of

heta

Solution: 👈: Video Solution

\tan \theta =

Perpendicular/Base

\sin \theta =

Perpendicular/hypotenuse

The height of the cloud in the lake from point

P

is also

2H

metres

In an

\triangle PAC

\tan 30^{\circ} = \frac{AC}{AP} = \frac{1}{\sqrt{3}}

\Rightarrow AP = H \sqrt{3}

In an

\triangle PAB

\tan \theta = \frac{AB}{AP} = \frac{H+2H}{H\sqrt{3}}

\Rightarrow \tan \theta = \sqrt{3} = \tan 60^{\circ}

\therefore \theta = 60^{\circ}

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