JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Heights and Distances

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

3 0^{\circ}

and the angle of depression of reflection of the cloud in the lake from P be

6 0^{\circ}

, then the height of the cloud (in meters) from the surface of the lake is :

(A)60
(B)50✓ Correct
(C)45
(D)42

Answer: (B)

Solution

Let the cloud stand

x

m above

P

with horizontal distance

y

. From the elevation,

tan 3 0^{\circ} = \frac{x}{y}

, so

y = 3 x

. The reflection lies

25 + x + 25 = 50 + x

below

P

, and from the depression

tan 6 0^{\circ} = \frac{50 + x}{y}

, so

3 y = 50 + x

. Substituting

y = 3 x

gives

3 x = 50 + x

, so

x = 25

m, and the cloud's height above the lake is

25 + 25 = 50

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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