Question

as observed from the top of a 75 metre Lighthouse from the sea level, angle of depression of two ships are 30 degree and 45 degree.if one ship is exactly behind the other on the same side Lighthouse, find the distance between the two ships

Answer 1

Hope this will help you

Answer 2

Answer:

$Distance=75(\sqrt{3}-1)\, m$

Step-by-step explanation:

In the figure, we can say that the angle of depression of two ships are 30 and 45 degrees.

Also,

Height of the Lighthouse, h = 75 m

and,

Distance between the two ships = x m

So,

In triangle ABC,

$tan\,45=\frac{AB}{BC}=\frac{75}{BC}\\1=\frac{45}{BC}\\BC=45\,m$

Similarly,

In triangle ABD,

$tan\,30=\frac{AB}{BD}\\\frac{1}{\sqrt{3}}=\frac{75}{BD}\\BD=75\sqrt{3}\,m$

Therefore,

The distance between the two ships is given by,

$x = BD-BC\\x=75\sqrt{3}-75\\x=75(\sqrt{3}-1)\, m$

Therefore, we can say that the distance between the two ships is,

$x=75(\sqrt{3}-1)\, m$