Question

the angle of elevation of a cloud from a point 10 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60 degree find the height of the cloud from the surface of the lake​

Answer 1

Step-by-step explanation:

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This is the Answer

Answer 2

Tip:

Angle of elevation: If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object.

Angle of depression: If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.

Recall the trigonometric ratios and their standard values

$\tan\theta=\frac{opposite\hspace side}{adjacentside}$

Given:

The angle of elevation from a point $10m$ above a lake $=30^ \circ$

The angle of depression of its reflection in the lake $=60^\circ$

Explanation:

Refer the figure

Let $OH=x$

$CD=OB=10m$

$AB=A'B=10+x$

In $\triangle ADO,$

$\tan 30^\circ=\frac{OA}{OD} \\\implies\frac{1}{\sqrt{3} } =\frac{x}{OD} \\\implies OD=\sqrt{3} x ..............(1)$

In $\triangle A'DO,$

$\tan 60^\circ=\frac{OA'}{OD} \\\implies{\sqrt{3} } =\frac{A'B+OB}{\sqrt{3} x} (from\hspace 11)\\ \implies3x=x+10+10\\\implies2x=20\\\implies x=10m$

The height of the cloud from the surface of the lake

$=OB+OA\\=10+10\\=20m$