From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is
Here AB is the light house of height h meters
The angles of depression from the light house are 30° and 45°
The distance between the two ships is CD
In Δ ABC
tan 45° =
⇒ BC = AB (∵ tan 45° = 1)
⇒ BC = h
In Δ ABD
tan 30° =
⇒ (h + CD) = √3 h (AB = BC = h)
⇒ CD = (√3 -1) h