As observed from the top of a lighthouse, 72 m high above sea the angle of depression of a ship changes from 45° to 60° in 10 seconds. The speed (in m/s ) of the ship is -

 3.0432

in triangle ABD

tan 45° = \(\frac{AB}{BD}\)

1 = \(\frac{AB}{BD}\)

As , AB = 72 m . so , BD is also 72m

in triangle ABC

tan 60° =  \(\frac{AB}{BC}\)

\(\sqrt{3}\)  = \(\frac{AB}{BC}\)

\(\sqrt{3}\)  = AB = 72 m

So  , BC = \(\frac{72}{\sqrt{3}}\)  = 24\(\sqrt{3}\)

The distance travelled by the ship = CD = BD - BC = 72 - 24\(\sqrt{3}\) =30.432 m

Distance  = Speed × Time

Speed = \(\frac{30.432}{10}\) = 3.0432 m/s