Some Applicatio...

If a flag-staff of $$6m$$ height placed on the top of a tower throws a shadow of $$2\sqrt { 3 } m$$ along the ground, then what is the angle that the sun makes with the ground?

The angle of elevation of the top of a tower from the top and bottom of a building of height $$a$$ are $$30^{\circ}$$ and $$45^{\circ}$$ respectively. If the tower and the building are at same level, the height of the tower is 

The angle of elevation of the top of pole from the point $$D$$ on the ground be $$\alpha$$, whereas the angle of elevation of the top of pole from the point which is at a height $$'b'$$ above point $$D$$ is $$\beta$$, then the length of pole is:

The angle of elevation of the top of an unfinished tower at a point $$120m$$ from its base is $$45^o$$. How much higher must the tower be raised so that its angle of elevation becomes $$60^o$$ at the same point?

$$ABCD$$ is a square plot. The angle of elevation of the top of a pole standing at $$D$$ from $$A$$ or $$C$$ is $$30^\circ$$ and that from $$B$$ is $$\theta$$, then $$\tan \theta$$ is equal to

From the top of a cliff of height $$a$$, the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height $$h$$. If $$\theta$$ be the angle of elevation then its value is:

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be $${30^ \circ }$$. After $$3\text{ min.}$$ this angle becomes $${60^ \circ }$$. After how much more time will the car reach the tree

A uniform rod is rested on a wall and its lower end is tied to the wall with the help of a horizontal string of negligible mass as shown. Length of rod is $$L$$ and height of the wall is $$h$$. What will be tension in the string? (all surface are frictionless)

From the top of a $$25\ \text{m}$$ high pillar at the top of tower, angle of elevation is same as the angle of depression of foot of tower,  then height of tower is: 

A ship $$A$$ is moving westward with a speed of $$10$$ km/s. and ship $$B$$ $$100$$ km south of $$A$$ is moving northward with a speed of $$10$$ km/hr. The time after which distance between then becomes shortest is: