Question

As observed from the top of a 60 m high lighthouse from the sea-level, the angles of depression of two ships are ${30}^o$ and ${45}^o$. If one ship is exactly behind the other on the same side of the lighthouse. Find the distance between the two ships.

• A. $20m$
  
• B. $46.5m$
  
• C. $54.9m$
  
• D. $60.1m$
  

Answer 1

The correct option is C $54.9m$

From the given figure
$tan{45}^o=\frac{75}{y}$
Hence
$y=75m$
And
$tan{30}^o=\frac{75}{75+x}$

$75+x=75\sqrt{3}$

$x=75(\sqrt{3}-1)m=54.9m$=Distance between the ships.