Some Applicatio...

The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30$$^\circ$$. If the angle of elevation at the same point is to be 45$$^\circ$$, then the pillar has to be raised to a height of how many metres?

Two men standing on opposite sides of a flag staff measure the angles of the top of the flagstaff as $$30^{\circ}$$ and$$\, 60^{\circ}$$. If the height of the flagstaff is $$18$$ $$m$$ the distance between the men is :  

At a certain instant the ratio of the lengths of a pillar and its shadow are in the ratio $$1 : \sqrt{3}$$ at that instant, the angle of elevation of the sun is:

Choose the correct answer from the alternatives given.
A tree is broken by the wind. If the top of the tree struck the ground at an angle of $$30^\circ$$ and at a distance of 30 m from the root, then the height of the tree is

The angle of elevation of a tower from a point is $${ 30 }^{ \circ}$$. At a point on the horizontal line passing through the foot of the tower and $$50$$ metres nearer it, the angle of elevation is $${ 60 }^{ \circ }$$. The distance of the first point from the tower is

Two beams of length $${l}_{1}$$ and $${l}_{2}$$ are leaning on opposite sides of a thin vertical wall meeting at the same point on the wall and making angles $${30}^{o}$$ and $${60}^{o}$$ with it respectively. Then $${l}_{2}$$ is equal to

A man on the top of a bamboo pole observes that the angle of depression of the base and the top of another pole are $${60}^{o}$$ and $${30}^{o}$$ respectively. If the second pole stands $$5$$ m above the ground level, then the height of the bamboo pole on which the man is sitting is

The angles of elevation of the top of a temple, from the foot and the top of a building $$30\ m$$ high, are $$60^{\circ}$$ and $$30^{\circ}$$ respectively. Then height of the temple is

A 25 m long ladder is placed against a vertical wall such that the foot of the ladder is 7 m from the feet of the wall. If the top of the ladder slides down by 4 cm, by how much distance will the foot of the ladder slide?

The angles of elevation of the top of a tower from two points A & B lying on the horizontal through the foot of the tower are respectively $$30^{\circ}$$ and $$45^{\circ}$$ of A & B are on the same side of the tower and AB = 48 m then the height of the tower is