Two ships are sailing in the sea on the two sides of a lighthouse The angle of elevation of the top ...........

Quantitative Aptitude ( CCS) Trignometry

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

273 m

100 m

258 m

300 m

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Explanation:

Let BD be the lighthouse and A and C be the positions of the ships.
Then, BD = 100 m, angle BAD = 30° , angle BCD = 45°
tan30°=BD/BA
⇒1/√3=100/BA
⇒BA=100√3
tan45°=BD/BC
⇒1=100/BC
⇒BC=100
Distance between the two ships
= AC = BA + BC
=100√3+100
=100(√3+1)
= 100(1.73+1) = 100 × 2.73 = 273 m