The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^o . At a point Y, 40 m vertically above X, the angle of elevation is 45^o . Find the height of the PQ and the distance XQ.

The angle of elevation of a jet fighter from a point A on the ground is 60^o . After a flight of 15 seconds, the angle of elevation changes to 30^o. If the jet is flying at a speed of 720 km/hr, find the constant height. \((\sqrt { 3 } =1.732)\) ^.

The angle of elevation of a cloud from a point 60 m above a lake is 30^o and the angle of depression of the reflection of the cloud in the lake is 60^o . Find the height of the cloud from the surface of the lake.

At the foot of a mountain, the elevation of its summit is 45^o . After ascending 1000 m towards the mountain up a slope of 30^o inclination, the elevation is found to be 60^o . Find the height of the mountain.

The pilot of an aircraft flying horizontally at a speed of 1200 km/hr. observes that the angle of depression of a point on the ground changes from 30^o to 45^o in 15 seconds. Find the height at which the aircraft is flying.

From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stones on the opposite sided of the aeroplane are found to be \(\alpha\) and \(\beta\), show that the height of the aeroplane is \(\frac { tan\alpha tan\beta }{ tan\alpha +tan\beta } \).

A tower subtends an angle \(\alpha\) at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b metres just above A is \(\beta\). Prove that the height of tower is b tan \(\alpha\cot\beta\).

The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60^o and 30^o respectively. Find the height of the balloon above the ground.

The shadow of a tower standing on a level ground is found to be 20m longer when the sun's altitude is 45^o than when it is 60^o Find the height of the tower.

A man in a boat rowing away from a lighthouse 100m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60\(\unicode{xb0} \) to 45\(\unicode{xb0} \) .Find the speed of the boat.