Question

As observed from the top of a 80 m tall lighthouse, the angles of depression of two ships, on the same side of a light house in a horizontal line with its base, are 30° and 40° respectively. Find the distance between the two ships. Give your answer corrected to the nearest metre.

Answer 1

Let AB represent the lighthouse.

Let the two ships be at point D and C having angle of depression 30° and 40° respectively.

Let x be the distance between the two ships. 

Clearly, m∠ACB = 40° and m∠ADB = 30°

In ΔACB

`tan 40^circ = 80/(CB)`

`=> CB = 80/ 0.84 = 95.24  m`

In ΔADB 

`tan 30^circ = 80/(DB)`

`=> DB = 80/(0.58) = 137.93  m`

DC = DB – CB

`=>` x = 137.93 – 95.24

`=>` x = 42.69 ≈ 43 m

The distance between the two ship is 43 m.