Question

As observed from the top of a 70 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use `sqrt(3)` = 1.73)

Answer 1

Let AB = lighthouse

C = II ship,

D = I ship

CD = x  ...(Let)

In right angle ΔACB

tan 45° = `(AB)/(BC)`

`1 = 70/(BC)`   ...(Given AB = 70 m)

BC = 70 m   ...(i)

In right angle ΔADB

tan 30° = `(AB)/(BD)`

tan 30° = `(AB)/(BC + CD)`

⇒ `1/sqrt(3) = 70/(70 + x)`  ....[From (i)]

⇒ `70 + x = 70sqrt(3)`

⇒ `x = 70sqrt(3) - 70`

⇒ `x = 70(sqrt(3) - 1)`

⇒ x = 70 × 0.73

⇒ x = 51.1 m