The angle of elevation of a cloud from a point 10 meters above the...

The angle of elevation of a cloud from a point

10

meters above the surface of a lake is

{30}^{o}

and the angle of depression of its reflection from that point is

{60}^{o}

. Then the height of the cloud above the lake is The angle of elevation of a cloud from a point 10 meters above the surface of a lake is 30 ^ o and the angle of

The angle of elevation of a cloud from a point 10 meters above the surface of a lake is 30 ^ o and the angle of

Options

A $20meters$
B $20\sqrt{3}meters$
C $\dfrac{20\left(\sqrt{3} - 1\right)}{\sqrt{3}}meters$
D $20\left(\sqrt{3} - 1\right)meters$

Correct answer

A. $20meters$

Step-by-step solution

Let

C

be the cloud,

D

its reflection and

PB

is the surface of the lake
Then,

PC = PD = H,

QA = \left(H - 10\right)cot {30}^{o} = \left(H + 10\right)cot {60}^{o}

H = 10\left(\dfrac{\cot 3{0}^{o} + \cot 6{0}^{o}}{\cot 3{0}^{o} - \cot 6{0}^{o}}\right) = \left[10\sin \left(9{0}^{o}\right)\right] / \sin \left(3{0}^{o}\right) = 20

meters

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