From the top of 120 m high lighthouse the angle of depression of two ships on opposite side of the b...........

Quantitative Aptitude (CPO) Height and Distance

From the top of 120 m high lighthouse, the angle of depression of two ships on opposite side of the base of the lighthouse is 30^oand

.60^o What is the distance between the ships? (rounded oft)

This questions was previously asked in

SSC CPO 14th-March-2019-Shift-1

327 m

177 m

277 m

127 m

- The problem considers a lighthouse with a height of 120 meters.

- There are two ships on opposite sides of the lighthouse's base.

- The angle of depression to one ship is 30°, and to the other, it is 60°.

- We can use trigonometry (specifically, tangent of angle) to find the horizontal distances from the lighthouse to each ship.

- Using the tangent for the 30° angle:

$$\tan(30°) = \frac{120}{d_1}$$, solving gives $d_1 = \frac{120}{\tan(30°)}$.

- Using the tangent for the 60° angle:

$$\tan(60°) = \frac{120}{d_2}$$, solving gives $d_2 = \frac{120}{\tan(60°)}$.

- Calculate $d_1$ and $d_2$, then add them to find the total distance between the ships.

- The calculation results in approximately 277 meters.

- The correct option is: Option 3: 277 meters

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