Some Applicatio...

The shadow of tower standing on a level ground is $$x\ m$$ long when the Sun's altitude is $$30^{\circ}$$, while it is $$y\ m$$ long when the altitude is $$60^{\circ}$$. If the height of the tower is $$45\cdot \dfrac {\sqrt {3}}{2}m$$, then $$x - y$$ is

A man on the top of a cliff 100 m high, observe the angles of depression of two points on the opposite sides of the cliff as 30$$^o$$ and 60$$^o$$ respectively. Then, the distance between the two points is equal to

Find the height of the chimney when it is found that  on walking towards it $$50$$ m in the horizontal line through its base, the angle of elevation of its top changes from $$30^{\circ}$$ and to $$60^{\circ}$$ 

A house subtends a right angle at the window of the opposite house and the angle of elevation of the window from the bottom of the first house is $$60^o$$. If the distance between the two houses be 6 m, then the height of the first house is?

Two posts are $$x$$ metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meters) of the shorter post is 

At a distance $$2h$$ $$m$$ from the foot of a tower of height $$h$$ $$m$$, the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

From a point $$\mathrm{a}$$ metre above the lake, the angle of elevation of a cloud is $$\alpha$$ and the angle of depression of its reflection is $$\beta$$, then height of the cloud is .......

At $$4:00$$ p.m. on a sunny day, a stick $$2$$ feet tall casts a shadow $$5$$ feet long. At the same time, a tree nearby casts a shadow $$55$$ feet long. What is the height in feet, of the tree ?

From an airplane flying vertically above a horizontal road, the angle of depression of two consecutive kilometer stones on the same side of the airplane are observed to be $${ 30 }^{ \circ }$$ and $${ 60 }^{ \circ}$$, respectively. The height at which the airplane is flying (in km) is:

The angle of elevation of the sum when the length of the shadow of a tower is equal to its height is: