Some Applicatio...

A straight tree breaks due to wind and the broken parts bends without getting detached such that the top of the tree touches the ground making an angle of 30$$^o$$ with the ground. The distance from the part of the tree to the point when the top touches the ground is 10 m. The height of the tree is _____.

The elevation of the top of a hill at each of the three angular points X, Y, Z of a horizontal $$\displaystyle \Delta XYZ$$ is $$\displaystyle \alpha $$, then the height of the hill is 

A tree $$10(2+\sqrt 3)$$ metres high is broken by the wind at a height $$10\sqrt 3$$ metres from its root in such a way that top struck the ground at certain angle and horizontal distance from the root of the tree to the point where the top meets the ground is $$10m$$. Find the angle of elevation made by top of the tree with the ground.

A man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of $$\displaystyle 45^{0}$$ with the man's eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes $$\displaystyle 30^{0}$$. What is the approximate speed of the boat assuming that it is running in still water?

The angle of elevation of the top of the tower from two points at distance $$a\ m$$ and $$b\ m$$ from the base and in the same straight line with it are complementary, then the height of the tower is 

$$AB$$ is a vertical pole. The end $$A$$ lies on the ground. $$C$$ is the midpoint of $$AB. P$$ is a point on the level ground such that the portion $$BC$$ subtends an angle $$\displaystyle  \phi $$ at $$P$$. If $$AP = nAB$$ then the value of $$\displaystyle  \cot \phi $$ is:    

Four point $$A, B, C, D$$ are in a plane so that $$B$$ is in the line joining $$A$$ and $$C$$ also $$B$$ is due north of $$D$$ and $$D$$ is due west of $$C$$. $$BD = 2$$, $$\displaystyle \angle BDA = 45^{\circ}$$ $$\displaystyle \angle BCD = 30^{\circ}$$. Then $$AD$$ equal to: 

On the ground level, the angle of elevation of a tower is $$ 30$$$$^o$$. On moving $$20$$ m nearer, the angle of elevation is $$60$$$$^o$$. The height of the tower is _____.

If the sun ray's inclination increases from $$\displaystyle  45^{\circ}$$ to $$\displaystyle  60^{\circ}$$ the length of the shadow of a tower decreases by $$50\ m$$. Find the height of the tower.

The angles of elevation of an aeroplane flying vertically above the ground from two consecutive milestones(1 km) apart are 45$$^o$$ and 60$$^o$$. The height of the aeroplane from the ground is _____