Exams › SSC CGL (Prelims) › General

From point C on the ground, the angle of elevation to the top of a cliff is 30°. From point D, which is 60 m closer to the cliff, the angle of elevation is 60°. Find the ratio of the distance of C from the cliff's foot to the distance of D from the cliff's foot.

1. 1:3
2. 2:1
3. 3:1
4. 4:1

Correct answer: 3:1

Solution

Let the distance of D from the cliff's foot be \(x\), so C is \(x+60\) m away. Using \(\tan 60^\circ = h/x\) and \(\tan 30^\circ = h/(x+60)\), we get \(h=\sqrt{3}x\) and \(h=(x+60)/\sqrt{3}\). Solving gives \(x=30\), so C:D = 90:30 = 3:1.

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