Question

A light house is 20m high. an observer on top of the light house observs a boat at an angle of depression 30°. how far is the boat from the observer.​

Answer 1

Answer:

Let AB=90 m represents the height of lighthouse. Point C represents the position of the ship.

Draw ray AM∥ seg BC

∠ACB is the angle of depression,

∠MAC=60o

Also, ∠ACB≃∠MAC    (Alernate angles)

∠ACB=60o

Let the distance of ship from the light-house be x metres.

In right angled ΔABC,

tan60o=x90

⇒x=390×33

=3903

=303

=30×1.73=51.9

∴ Distance of the ship from the lighthouse is 51.9 m.

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