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The angle of elevation of a cloud from a point 200 meter above a water body is 30° and the angle of depression of its reflection in the water body is 60°. The height of the cloud in meter is:

Solution

✅ Correct Option: 4

Let the cloud be hh above the water and dd the horizontal distance. Then (h−200)/d=tan⁡30(h-200)/d = \tan 30 and (h+200)/d=tan⁡60(h+200)/d = \tan 60.

Dividing, (h+200)/(h−200)=3(h+200)/(h-200) = 3, so h=400h = 400 m above the water, i.e. 400−200=200400 - 200 = 200 m above the point of observation.

Note: The phrase 'height of the cloud' is open to two readings; we have taken it as the height above the observation point, which matches the given options.

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