The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x: y.
In ΔABE
tan 30° = x/a
⇒ x = a tan 30°
Now, in Δ ECD
tan 60° = y/a
⇒ y = a tan 60°
⇒ x :y = 1:3