A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45^o . The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes 30^o . Find the speed of flying of the bird.

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.

A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches a height of 90 m on the wall and makes an angle of 60^o with the ground. If while resting at the same point on the path, it were made to lean against the other wall, it would have made an angle of 45^o with the ground. Find the height it would have reached on the second wall.

Two stations due south of a leaning tower which leans towards north are at distances a and b from its foot. If \(\alpha\) and \(\beta\) be the elevation  of the top of the tower from these stations, prove that its inclination \(\theta\) to the horizontal is given by \(cot\theta =\frac { b\quad cot\alpha -a\quad cot\beta }{ b-a } \).

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 \(\frac { tan\alpha tan\beta }{ tan\alpha +tan\beta } \).

From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be \(\alpha\) and \(\beta\) (\(\alpha\) > \(\beta\)). If the distance between the objects is 'p' metres, show that the height 'h' of the tower is given by \(h=\frac { p\quad tan\alpha \quad tan\beta }{ tan\alpha -tan\beta } \) . Also determine the height of the tower, if p = 50 m,\(\alpha\) = 60^o,\(\beta\)=30^o. 

From top of a 7m high building, the angle of elevation of the top of a cable tower is 60⁰ and the angle of depression of its foot is 45^o. Determine the height of the tower.

If the shadow of a tower 30m long, when the sun's elevation is 30⁰.What is the length of the shadow, when sun's elevation is 60⁰ ?

The length of the shadow of a tower standing on level ground is found to 2x meter longer when the sun,s altitude is 30^o than when it was 45^o. Prove that the height of tower is (\(\sqrt{3}+1\) )x metres .

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive kilometre stone on opposite sides of the aeroplane are observed to be 60⁰ and 30⁰ show that height (in metres) of aeroplane above the road is \(\sqrt{3}\over4\)km.