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Question:

If the angle of elevation of a cloud from a point P which is 25m above a lake be 30° and the angle of depression of reflection of the cloud in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is:

50

45

60

42

Solution:

tan30°=x/y ⇒y=√3x.. (i)
tan60°=(25+x)/(25+y) ⇒√3y=50+x ⇒3x=50+x ⇒x=25 m
∴Height of cloud from surface = 25 + 25 = 50 m