The angle of elevation of a cloud from a point 60m above the lake is 30 and the angle of - Maths - Some Applications of Trigonometry

Question

The angle of elevation of a cloud from a point 60m above the
lake is 30 and the angle of depression of its reflection in the
lake is 60 find the height of the cloud above the lake?

Rayya Halim · Accepted Answer

Let AO = H

CD = OB = 60 m

A' B = AB = 60 + H

In ∆ AOD,

$\tan 30 � = \frac{AO}{OD} = \frac{H}{OD} H = \frac{OD}{\sqrt{3}} OD= \sqrt{3} H$

Now, In ∆ A'OD,

$\tan 60 � = \frac{OA'}{OD} = \frac{OB+BA'}{OD} \sqrt{3} = \frac{60 + 60 + H}{\sqrt{3} H} = \frac{120 + H}{\sqrt{3} H}$

⇒ 120 + H = 3H

⇒ 2H = 120

⇒ H = 60 m

Thus, height of the cloud above the lake = AB + A'B = 60 + 60 = 120 m.

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The angle of elevation of a cloud from a point 60m above the lake is 30 and the angle of depression of its reflection in the lake is 60.find the height of the cloud above the lake?