JEE Main · 2004 · 24 Apr 2004 · Offline · Heights and Distances

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A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is

6 0^{\circ}

and when he retires 40 meter away from the tree the angle of elevation becomes

3 0^{\circ}

. The breadth of the river is

(A)20 m✓ Correct
(B)30 m
(C)40 m
(D)60 m

Answer: (A)

Solution

Let the river's breadth be

d

and the tree's height

h

. From the near bank,

tan 6 0^{\circ} = \frac{h}{d}

, so

h = d 3

. After stepping back

40

metres,

tan 3 0^{\circ} = \frac{h}{d + 40}

, so

h = \frac{d + 40}{3}

. Equating the two,

d 3 = \frac{d + 40}{3}

, i.e.

3 d = d + 40

, which gives

d = 20

metres.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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