Question

Two ships are there in the sea on either side of a light house in such away that the ships and the light house are in the same straight line. The angles of depression of two ships are observed from the top of the light house are ${60}^0$ and ${45}^0$ respectively. If the height of the light house is $200$ m, find the distance between the two ships. (Use $\sqrt{3}=1.73$)

Answer 1

Given the Height of the Light House $AD=200m$

Let the Position of the Ships be $C$ and $B$

Now, in $△ACD$

$\tan {60}^o=\frac{200}{DC}\Rightarrow DC=\frac{200}{\sqrt{3}}=115.6$

and in $△ABD$

$\tan {45}^o=\frac{200}{BD}\Rightarrow BD=200$

Distance between the Ships $=BC=DB+BC=200+115.6=315.6m$