From the top of a vertical cliff an observer sees two boats A and B. The angles of elevation from A and B to O are respectively, \({45^\circ}\) and \({60^\circ}\). Given that the boats are 100 m apart, find the height of the cliff to the nearest metre.

Two observers A and C are 100 m apart on a straight road. They observe a balloon at angles of elevation \({42^o}\) and \({58^o}\) respectively. Find the height of the balloon above the road.

(Give your answer to the nearest metre)

The angle of depression from the top of a cliff to a small boat, 800 m from the base of the cliff is \({\rm{6}}^\circ \). Find the height of the cliff.

A rocket launched vertically from \(A\) is observed from \(B\).

Soon after the launch when at position \(\mathrm{C}\) its angle of elevation is \(30^{\circ}\). After it climbs 5000 metres from this position to \(D\) its angle of elevation is \(65^{\circ}\)

i) Find \(\mathrm{BC}\) to the nearest metre.

ii) Find how far the observer is from the launching pad to the nearest metre.

A man of 175cm height casts a shadow 190 cm long. Calculate, correct to the nearest degree, the angle of elevation of the sun at this time of day.

The angle of depression from an observer from the top of a cliff to a row boat is \({\rm{6}}^\circ \) . The cliff is 25m above sea level. The horizontal distance from the boat to the cliff is?

The angle of elevation from a marker on level ground to the top of a building 100m high is \({\rm{22}}^\circ \). Find the distance the marker must be moved so that the angle of elevation is \({\rm{40}}^\circ \).

An observer notices a plane flying directly overhead.Two minutes later the plane is at an angle of elevation of \({\rm{27}}^\circ \).After a further 2 minutes the angle of elevation is?