Question

The angle of depression of two ships from the top of light house situated at 60 m height from sea-level, are 30° and 45° if two ships are on the same side of the light house, then find the distance between two ships.

Answer 1

Let AB is a light house of height 60 m and point C and D are two position of ships.

One ship is exactly behind the other on the same side of the light house. 

The angle of depression of two ships 30° and 45°.

∠PAC = 300 and ∠PAD = 45°

∠ACD = ∠PAC = 30° (alternate angle)

∠ADB = ∠PAD = 45° (alternate angle)

Let CD = x m

From right angled ∆ABD,

tan 45° = AB/BD

1 = 60/BD

⇒ BD = 60 m …..(i)

From right angled ∆ABC,

[∵ From equation (i) BD = 60 m]

x + 60 = 60√3

x = 60√3 – 60

= 60(√3 – 1)

= 60 × (1.732 – 1)

= 60 × 0.732

= 43.92 m

Hence, distance between two ships = 43.92 m