Some Applicatio...

The angle of elevation of a cloud from a point $$h$$ metres above the lake water level is $$\theta$$ and the angle of depresion of its image in the lake is $$\phi$$. The height of the cloud is

$$A$$ and $$B$$ are two stations due north and south of a tower of height $$25m$$. The angles of depression of the stations from the top of the towe $$r$$ observed to be $$30^{0}$$ and $$45^{0}$$ respectively. The distance between the two stations is

The angle of elevation of a cliff from a point $$A$$ on the ground and from the point $$B$$ $$100\ m$$ vertically above $$A$$ are $$\alpha$$ and $$\beta$$ respectively. The height of the cliff (in metres) is

From the top of a cliff $$24\ m$$ height, a man observes the angle of depression of a boat is to be $$60^{\circ}$$. The distance of the boat from the foot of the cliff is

From the top of a tower, $$80\text{ m}$$ high, the angles of depression of two points $$P$$ and $$Q$$ in the same vertical plane with the tower are $$45^{^\circ}$$ and $$75^{^\circ}$$ respectively, find the value of $$PQ.$$

In a prison wall there is a window of $$1$$ metre height, $$24$$ metres from the ground. An observer at a height of $$10 m$$ from ground, standing at a distance from the wall finds the angle of elevation of the top of the window and the top of the wall to be $$45^{ 0}$$ and $$60^{0}$$ respectively. The height of the wall above the window is

If from the top of a tower of $$60$$ metre high, the angles of depression of the top and floor of a house are $$\alpha$$ and $$\beta$$ respetivley and if the height of the house is $$\displaystyle \frac{60\sin(\beta-\alpha)}{x}$$, then $$x=$$

On the level ground the angle of elevation of the top of a tower is $$30^{0 }$$ On moving 20 metres nearer tower, the angle of elevation is found to be $$60^{0}$$ The height of the towerin metres is

The angle of elevation of the top of a hill when observed from a certain point on the horizontal plane through its base is $$30^{0}$$. After walking 120 meters towards it on level ground the elevation is found to be $$60^{0}$$. Find the height of the hill(in meters).

$$A$$ man observes a tower$$AB$$ of height $$h$$ from a point $$P$$ on the ground. He moves a distance $$d$$ towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance $$\dfrac {3d}{4}$$ in the same direction and the angle of elevation is three times that at $$P$$. Then $$\displaystyle \frac{h^{2}}{d^{2}}=$$