The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water – surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water – surface of the lake is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 60 m
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Application |
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From the figure:
Suppose the height of aeroplane from the water surface BC = h cm And AP = BQ = 30 cm ⇒ CQ = DQ = h + 30 So, BD = 30 + h + 30 = (h + 60) In triangle ABC: tan 30 = CB/AB ⇒ 1/√3 = h/AB ⇒ AB = √3h ………………… (1) In triangle ABD: tan 60 = BD/AB ⇒ √3 = (h + 60)/AB ⇒ AB = (h + 60)/√3 ……… (2) From equation 1 and 2: √3h = (h + 60)/√3 ⇒ 3h = h + 60 ⇒ 2h = 60 ⇒ h = 30 Hence, Height of aeroplane from the surface of water: CQ = 30 + 30 = 60 m |
