Some Applicatio...

Statement $$I$$: $$A$$ kite is flying with the string inclined at $$30^{0}$$ to the horizontal. The height of the kite above the ground when the string is $$15$$ mt long is $$7.5$$ mts.
Statement $$II$$: The altitude of the sun is $$45^{0}$$, When the length of the shadow of a pole is same as height of the pole.

The angle of elevation of the top of the tower at any point of the ground is $${30}^{0}$$ and if moving $$20m$$ towards the tower it becomes $${60}^{0},$$ then the height of the tower is 

A balloon moving in a straight line passes vertically above two points $$A$$ and $$B$$ on horizontal plane $$1000\ ft$$ apart. When above $$A$$ it has an altitude of $$60^{0}$$ as seen from $$B$$. When above $$B$$ it has an altitude of $$45^{0}$$ as seen from $$A$$. The distance of $$B$$ from the point at which it will touch the plane is

The top of hill observed from the top and bottom of a building of height $$h$$ is at the angles of elevation $$p$$ and $$q$$ respectively. The height of the hill is

Three points$$A,\ B,\ C$$ are on the straight bank of a river such that $$=BC=2$$ Km. $$A$$ boat is moving towards $$B$$ on a line at right angles to the bank. At some point $$AC$$ subtends an angle of $$60^{0}$$ After moving for 10 minutes in the same direction $$AC$$ subtends an angle of $$120^{0}$$. The speed of boat is

An observer finds that the angular elevation of a tower is $$\theta$$. On advancing $$a$$ metres towards the tower, the elevation is $$45^{0}$$ and on advancing $$b$$ metres nearer the elevation is $$ 90^{0}-\theta$$, then the height of the tower (in metres) is

Tower is observed from two stations $$A$$and $$B$$ where $$B$$ is East of $$A$$ at a distance $$100m$$. The tower is to north of $$A$$ and to North-West of $$B$$. The angles of elevation of the tower from $$A$$and $$B$$ are complementary. The height of the tower (in meters) is:

An aeroplane flying horizontally $$1$$ km above the ground is observed at an elevation of $$60^{0}$$. If after $$10$$ secs the elevation is observed to be $$30^{0}$$. Then the uniform speed per hour the aeroplane is

A balloon moving in a straight line passes vertically above two points $$A$$ and $$B$$, on a horizontal plane, $$1000\ ft$$ apart. When above $$A$$, it has an altitude of $$60^{0}$$ as seen from $$B$$ and when above $$B$$ it has an altitude of $$45^{0}$$ as seen from $$A$$. The distance, from $$A$$, of the point at which it will touch the plane is

At the foot of a mountain the angle of elevation of a summit is found to be $$45^{ 0}$$. After ascending $$1$$ km towards the mountain up. On a slope of inclination $$30^{0}$$, the angle of elevation is found to be $$60^{0}$$. The height of the mountain is