Some Applicatio...

The angle of elevation of a cloud from a point 100 meter above the surface of a lake is $$30^0$$ and the angle of depression of its image in the lake is $$60^0$$ then height of the cloud above the lake is 

The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of $$30^o$$ with horizontal, then the length of the wire is 

The angle of elevation of stationary cloud from a point 25 ml above the lake is $$ 15^0$$ and the angle of depression of reflection  in the lake is $$45^0$$ .Then the height of the cloud above the level 

The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle 0 with level ground such that $$tan\, \theta = \frac {15}{8}$$, how high is the kite ? 

A man observes two objects in a line in the west. On walking a distance $$x $$ towards the north, the objects subtends an angle $$\alpha$$ in front of him and on walking a further distance $$x$$ to north they subtend an angle, $$\beta$$, then the distance between the objects is

A sphere with centre $$O$$ sits atop of pole as shown in the figure. An observer on the ground is at a distance $$50m$$ from the foot of the pole. She notes that the angles of elevation from the observer to points $$P$$ and $$Q$$ on the sphere are $$30^{\circ}$$ and $$60^{\circ}$$, respectively. Then, the radius of the sphere in meters is

One side of a rectangular piece of paper is $$6\text{ cm}$$, the adjacent sides being longer than $$6\text{ cm}$$. One corner of the paper is folded so that it sets on the opposite longer side. If the length of the crease is $$l$$ $$\text{cm}$$ and it makes an angle $$\theta$$ with the long side as shown, then $$l$$ is

An observer standing at a point $$P$$ on the top of a hill near the sea-shore notices that the angle of depression of a ship moving towards the hill in a straight line at constant speed is $${30}^{o}$$. After 45 minutes, this angle becomes $${45}^{o}$$. If T (in minutes) is the total time taken by the ship to move to a point in the sea where the angle of depression from $$P$$ of the ship is $${60}^{o}$$, then T is equal to:

The height of a house subtends a right angle at opposite window from the base of the house is $$60^0$$. If the width of the road be 6 metres, then the height of the house is

From the top of aspire the angle of depression of the top and bottom of a tower of height h are $$\theta$$ and $$\phi$$ respectively. Then height of the spire and its horizontal distance from the tower are respectively.