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  • As observed from the top of a lighthouse, 75 m high from the sea level, the angles of depression of two ships are and

As observed from the top of a lighthouse, 75 m high from the sea level, the angles of depression of two ships are 30^{\circ} and 45^{\circ}. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

 

 

 

 
 
 
 
 

Answers (1)

Height of light house AD = 75 \; m

In right angled triangle ACD,

\tan C = \frac{AD}{CD}

\tan 45 = \frac{AD}{CD}

1 = \frac{AD}{CD}

CD = 75 \; m \;\;\; (\because AD =75)

In  \bigtriangleup AB\!D

\tan B = \frac{AD}{BD}

\tan 30 = \frac{AD}{BD}

\frac{1}{ \sqrt{3} } = \frac{75}{BD}

BD=75\sqrt{3}

BC+CD = 75\sqrt{3}

BC+75 = 75\sqrt{3}

BC = 75(\sqrt{3}-1) \; m

Hence the distance between two ships is 75(\sqrt{3}-1) \; m.

 

Posted by

Ravindra Pindel

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