Multiple Choice Questions

As observed from the top of a lighthouse 45 m high above the sea level the angle of depression of a ...........

Quantitative Aptitude (CPO) Height and Distance

As observed from the top of a lighthouse, 45 m high above the sea-level, the angle of depression of a ship, sailing directly towardsit,

changes from 30^o to 45^o. The distance travelled by the ship during the period of observation is: (Your answer

should be correct to one decimalplace.)

This questions was previously asked in

SSC CPO 11th Dec 2019 Shift-2

32.9 m

33.4 m

36.9 m

24.8 m

- To find the distance the ship traveled, we can use trigonometry.

- At 45 meters high, the angle of depression changes from 30° to 45° as the ship moves.

- Using the tangent function: tan(angle) = opposite/adjacent.

- Initially, tan(30°) = 45/distance1. Solving for distance1 gives distance1 = 45/tan(30°) = 45/v3/3 = 45v3.

- Finally, the angle of depression is 45°: tan(45°) = 45/distance2, hence distance2 = 45.

- The distance traveled by the ship is distance1 - distance2 = 45v3 - 45.

- Calculated, this is approximately 33.4 meters.

- Option 2 - 33.4 m is the correct answer.

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