Question

from the top of a lighthouse the angle of depression of two ships on the opposite sides of it are observed to be 30 degree and 60 degree.if the height of the light house is h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ships is 4/root 3 h metres

Answer 1

See the attached file

Answer 2

Answer:

$\frac{4}{\sqrt{3}}h$

Step-by-step explanation:

Refer the attached figure

Height of the light house =AC = h meters

BC is the distance between light house and ship 1

CD is the distance between lighthouse and ship 2

The angle of depression of two ships on the opposite sides of it are observed to be 30 degree and 60 degree

In ΔABC

Using trigonometric ratio

$tan \theta = \frac{Perpendicular}{Base}$

$tan30^{\circ}= \frac{AC}{BC}$

$\frac{1}{\sqrt{3}}= \frac{h}{BC}$

$BC= \sqrt{3}h$

In ΔACD

Using trigonometric ratio

$tan \theta = \frac{Perpendicular}{Base}$

$tan60^{\circ}= \frac{AC}{CD}$

$\sqrt{3}= \frac{h}{CD}$

$CD= \frac{h}{\sqrt{3}}$

So, distance between two ships = BC +CD = $\sqrt{3}h+\frac{h}{\sqrt{3}}=\frac{4}{\sqrt{3}}h$

Hence distance between two ships is $\frac{4}{\sqrt{3}}h$