Some Applicatio...

A baloon is observed simultaneously from three points $$A, B$$ and $$C$$ on straight road directly under it. The angular elevation at $$B$$ is twice and at $$C$$ is thrice that of $$A$$. If the distance between $$A$$ and $$B$$ is $$200 \,m$$ and the distance between $$B$$ and $$C$$ is $$100 \,m$$, then the height of ballon is

As observed from the top of a light house $$100$$m high from sea-level, the angles of depression of two ships are $$30^0$$ and $$45^0$$. If the ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use $$\sqrt3 = 1.732$$)

A man of height $$6$$ ft. observed the top of a tower at  the top and the foot of a pole of height $$10 ft.$$ are $$45^o$$ and $$30^o$$ of elevation and depression respectively. The height of the tower is :

Length of the shadow of a $$20$$ meters high pole is $$20$$ meter at $$7.30^{o}am$$. The angle of elevation of the sun rays with the ground?

The angle of elevation of the top of a tower at any point on the ground is $$\dfrac{\pi}{6}$$ and after moving $$20$$ meters towards the tower it becomes $${\pi}{3}$$.The height of the tower is equal to :

If the elevation of the sun is $$30^0$$, then the length of the shadow cast by a tower of $$150$$ ft height is :

A boy standing on the ground, spots a balloon moving with the wind in a horizontal line at a constant height. The angle of elevation of the balloon from the boy at an instant is $$60^{\circ}$$. After 2 minutes, from the same point of observation, the angle of elevation reduces to $$30^{\circ}$$. If the speed of wind is $$29\sqrt{3}$$ m/min. then, find the height of the balloon from the ground level.

The angle of elevation of the top of the tower at the eye of an observer is found to be $$45^{o}$$. Find the height of the observer, if he is standing at a distance of $$32.4\ m$$ away from the tower and the height of the tower is $$34\ m $$.

As observed from the top of a $$75\ m$$ high lighthouse from the sea-level, the angles of depression of two ships arc $$30^{o}$$ and $$45^{o}$$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. 

A man standing on a horizontal plane, observations the angle of elevation of the top of a tower to be $$\alpha$$. After walking a distance equal to double the height of the tower, the angle of elevation becomes $$2\alpha$$, then $$\alpha$$ is -