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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 30o and 45o. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use 3=1.732]

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Solution

Let, height of light house from sea level (AB)=100m
Let, two ships be at the positions be C and D
In ABC,
tan 45=ABBC
1=100BC
BC=100m
In ABD,
tan 30=ABBD
13=ABBD
BD=AB×3
=100×3
=173.2[3=1.732]
CD=BDBC=173.2=100=73.2m
the distance between two ships 73.2 m



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