Some Applicatio...

The lower window of a house is at $$2\ m$$ above the ground and its upper window is $$4\ m$$ vertically above the lower window. At certain instant the angle of elevation of balloon from these windows are observed to be $$60^0$$ and $$30^0$$ respectively. Then the height of the balloon above ground is

The angle of elevation of the top of a tower from the top and bottom of a building of height $$a$$ are $${0}^{o}$$ and $${45}^{o}$$ respectively. If the tower and the building stand at the same level, then height of tower is:

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle $$30^o$$ with it. The distance between the foot of the tree to the point where the top touches the ground is $$8\ m.$$ Find the height of the tree.

A tower  $${T_1}$$  of height 60m is located exactly opposite to a tower $${T_2}$$  of height 80m on a straight road. From the top of  $${T_1}$$   , if the angle of depression of the foot of  $${T_2}$$ , is twice the angle of elevation of the top of $${T_1}$$ , then the width (in m) of the road between the feet of the towers     $${T_1}$$ and $${T_1}$$   is: 

An electrician has to repair an electric fault on a pole of height $$5$$m. She needs to reach a point $$1.3$$m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of $$60^0$$ to the horizontal, would enable her to reach the required position? Also, how far the foot of the pole should she place the foot of the ladder? ( You may take $$\sqrt3=1.73$$).

From the top of a building $$15\text{ m}$$  high the angle of elevation of the top a tower is found to be $$30^\circ$$. From the bottom of the same building, the angle of elevation of the tower id found to be $$60^\circ$$. Find the height of the tower and the distance between the tower and the building.

The angle of elevation of the top of two points at a distance of $$9$$ m and $$16$$ m from the base of the tower and in the same straight line in the same direction with it are complimentary. Then the height of the tower is 

The angle of elevation of a jet plane 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 plane is flying at a constant height of $$1500\sqrt{3}\ meters$$. Find the speed of jet plane $$(\sqrt{3}=1.732)$$.

A boy is flying a kite with a string of length $$100$$ m. If the string is tight and the angle of elevation of the kite is $$26^032'$$, find the height of the kite correct to one decimal place (ignore the height of the boy).

From the point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are $$30^\circ$$ and $$45^\circ$$, respectively. If the bridge is at a height of $$3\ m$$ from the banks, find the width of the river.