Some Applicatio...

A pole $$6\ \text{m}$$ high casts a shadow of $$2$$$$\sqrt 3\text{ m}$$ on the ground. At that instance, the sun's elevation is :

From the base of a tower the angle of elevation of the top of the cliff is 60$$^o$$ and from the base of the cliff, the angle of elevation of the top a tower is 30$$^o$$. If the height of the tower is 50 m, then the height of the cliff is :

A boat is being rowed away from a cliff $$150$$ m high. From the top of the cliff, the angle of depression of the boat changes from 60$$^o$$ to 45$$^o$$ in 1 minute. If $$\sqrt3 = 1.73$$, the speed of the boat is _____

Two points at distance x and y from the base point are on the same side of the line passing through the base pf a tower. The angle of elevation from these two points to the top of the tower are complementary. Then, the height of the tower is :

The angle of elevation of the top of a tower at a distance 30 m from its foot on a horizontal plane is found to be 30$$^o$$. The height of the tower is _____

From the top of a tower, the angle of depression of a man standing 40 m away from the tower is 45. Then the height of the tower is:

A ladder is leaning against a wall such that its upper end touches the wall of the height of 3 m and the ladder is inclined at an angle having measure of 30$$^o$$ with the ground. The length of the ladder is:

From the top of a hill $$h$$ metres high the angles of depressions of the top and the bottom of a pillar are $$\alpha$$ and $$ \beta $$ respectively. The height (in metres) of the pillar is

$$P$$ is a point on the segment joining the feet of two vertical poles of heights $$a$$ and $$b$$. The angles of elevation of the tops of the poles from $$P$$ are $$45^0$$ each. Then, the square of the distance between the tops of the poles is

A person observes  the top of a tower from a point $$A$$ on the ground. The elevation of the tower from this point is $$60^{\circ}$$. He moves $$60\ m$$ in the direction perpendicular to the line joining $$A$$ and base of the tower. The angle of elevation of the tower from the point is $$45^{\circ}$$. Then the height of the tower (in meters) is