From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is

Question

From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be &#x3B1; and &#x3B2;. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is

Philoid · Accepted Answer

In the fig AB is the light house of height h (m)

In ∆ADC

tan β =

h = y tan β or y = ………………..(1)

In ∆ADB

tan α =

h = x tan α or x = …………….(2)

The distance between the two ships is BC = x + y

On adding eqn (1) & (2) we get,

x + y = +

⇒

meters PROVED