Some Applicatio...

Two vertical poles $$20m$$ and $$80m$$ high stand a part on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is

On one side of a road of width $$d$$ metres there is a point of observation $$P$$ at a height $$h$$ metres from the ground. If a tree on the other side of the road, makes a right angle at $$P$$, height of the tree in metres is:

A vertical tower of height $$50$$ meters high stands on a sloping ground. The bottom of the tower is at the same level as the middle point of a vertical flagpole. From the top of the tower, the angles of depression of the top and bottom of the flagpole are $$15^{0}$$ and $$45^{0}$$ respectively. The height of the flagpole is

The height of a hill is $$3,300$$ metres. From the point $$D$$ on the ground the angle of elevation of the top of the hill is $$60^{0}$$. A balloon is moving with constant speed vertically upwards from $$D.$$ After $$5$$ minutes of its movement a person sitting in it observes the angle of elevation of the top of the hill as $$30^{0}$$. The speed of the balloon is

Two light posts are of equal height. A person standing mid-way between the line joining their feet, observes the elevation of the posts to be $$30^{0}$$. After walking $$12$$ metres towards one of them, he observes that the same post now subtends an angle of $$60^{0}$$. Find the distance between them.

The angle of elevation of a tower from a point $$A$$ due south of it, is $$x$$, from a point $$B$$ due east of $$A$$, is $$y$$. If $$AB=l,$$ then the height $$h$$ of the tower is given by

A pole 6 m high casts a shadow $$2\sqrt{3}$$ m long on the ground, then the Sun's elevation is

The angle of elevation a vertical tower standing inside a triangular at the vertices of the field are each equal to $$\theta$$. If the length of the sides of the field are $$30\ m,\ 50\ m$$ and $$70\ m$$, the height of the tower is:

Two vertical poles $$20\ m$$ and $$80\ m$$ high stand apart $$50m$$ on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is

Two poles of height $$a$$ and $$b$$ stand at the centres of two circular plots which touch each other externally at a point and the two poles subtends angles of $$30^{o}$$ and $$60^{o}$$ respectively at this point. Then the distance between the centres of these plots is: