Question

As observed from the top of the light house, 100m above sea level, the angle of depression of a ship, sailing directly towards it, change from 30degree to 45degree. Find the distance travelled by the ship during the period of observation.

Answer 1

SOLUTION

Let A & B be two Position of the ship.

Then AB = d

Let observer be the point O the top of the light house PO

=) PO = 100m (Given)

Given,

Angle OAP = 30°

angle OBP = 45°

In ∆OPB

=) tan 45°= OP/BP

=) 1= 100/BP

=) BP= 100m

In ∆OPA

=)tan 30° = OP/AP

=) 1/√3= 100/d+ BP

=) 1/√3= 100/d+100

Solving

=) d= 73.2 metres

hope it helps ✔️

Answer 2

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