An observer 1.5 m tall is 20.5 meters away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

From a point P on the ground, the angle of elevation of the top of a 10 m tall building and a helicopter, hovering over the top of the building are 30° and 60° respectively. Find the height of the helicopter above the ground.

An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at the instant.

The upper part of a tree broken by wind, falls to the ground without being detached. The top of the broken part touches the ground at an angle of 38° 30' at a point 6 m from the foot of the tree. Calculate :

(i) the height at which the tree is broken.

(ii) the original height of the tree correct to two decimal places.