Question

From the top of a light house 100 m high, the angles of depression of two ships are observed as 48° and 36° respectively. Find the distance between the two ships (in the nearest metre) if:

1. the ships are on the same side of the light house,
2. the ships are on the opposite sides of the light house.

Answer 1

Let AB the light house.

Let the two ship be C and D such that ∠ADB = 36° and ∠ACB = 48°

In ΔABC,

`(AB)/(BC) = tan 48^circ`

`=> BC = 100/(1.1106) = 90.04  m `

In ΔABD,

`(AB)/(BD) = tan 36^circ`

`=> BD = 100/ 0.7265 = 137.64  m`

i. If the ships are on the same side of the light house, then distance between the two ships = BD – BC = 48 m

ii. If the ships are on the opposite side of the light house, then distance between the two ships = BD + BC = 228 m.