Question

As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30 degree and 45 degree. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships.

Answer 1

Answer:

height of  lighthouse = 100m

let distance travelled by the ship when the angle of depression changes from 60 to 30

DC= Y and distance BC = X

Then[ in right ∆ABC

tan 60=AB/BC

√3 = 100/x

x√3 =100

x= 100/√3......................(i)

in right ∆ ABD

tan 30 =AB/BD

1/√3 = 100/x+y

x+y =100√3 .................(ii)

From (i) and (ii) , we get

100√3+ y =100√3

y= 100√3 - 100/√3

100×3-100/√3

200/√3

y= 200/ 1.732

200.000/1732

distance traveled by the ship

= 115.47

Tip: use √3 = 1.732

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@GauravSaxena01