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If the angle of elevation of a cloud from a point P which is 25 m above a lake be $30^{\circ}$ and the angle of depression of reflection of the cloud in the lake from P be $60^{\circ}$ , then the height oif the cloud (in meters) from the surface of the lake is :
Option 1)
$45$
Option 2)
$60$
Option 3)
$42$
Option 4)
$50$

Answers (1)

best_answer

Trigonometric Ratios of Functions -

$\sin \Theta = \frac{Opp}{Hyp}$

$\cos \Theta = \frac{Base}{Hyp}$

$\tan \Theta = \frac{Opp}{Base}$

- wherein

Trigonometric Ratios of Functions

Angle of Elevation -

If an object is above the horizontal line from the eye, we have to raise our head to view the object.

- wherein

angle of elevation

$tan30^{0}=\frac{x-25}{d}$

$\frac{1}{\sqrt{3}}=\frac{x-25}{d}$

$d=\sqrt{3}\left ( x-25 \right )$

$tan\: 60=\frac{x+25}{d}$

$\Rightarrow d=\frac{x+25}{\sqrt{3}}$

$\sqrt{3}\left ( x-25 \right )=\frac{x+25}{\sqrt{3}}$

$\Rightarrow x=50m$

Option 1)

$45$

Option 2)

$60$

Option 3)

$42$

Option 4)
$50$

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