If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30 o and the angle of…

If the angle of elevation of a cloud from a point P which is 25m above a lake be 30o and the angle of depression of reflection of the could in the lake from P be 60o, then the height of the cloud (in meters) from the surface of the lake is :
  1. 50
  2. 60
  3. 45
  4. 42

Solution

tan⁡30o=x-25d

and tan⁡60o=x+25d

⇒tan⁡30otan⁡60o=x-25x+25⇒13=x-25x+25

⇒x+25=3x-75

⇒2x=100⇒x=50m

Asked in: JEE Main 2019 (12 Jan Shift 2)

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