A contractor wants to set up a slide for the children to play in the park. He wants to set it up at the height of 2 m and by making an angle of `30^(@)` with the ground. What should be the length of the slide?

A constractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5m, and is inclined at an angle of 30^(@) to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60^(@) to the ground. What should be the length of the slide in each case ?

You want to erect a pole of height 10 m with the support of three ropes. Each rope has to make an angle 30^(@) with the pole. What should be the length of the rope?

An electrician wants to repair an electric connection on a pole of height 9 m. He needs to reach 1.8 m below the top of the pole to do repair work. What should be the length of the ladder which he should use, when he climbs it at an angle of 60^(@) with the ground? What will be the distance between foot of the ladder and foot of the pole?

A swimmer starts to swim from point a to cross a river. He wants to reach point B on the opposite side of the river. The line AB makes an angle 60^(@) with the river flow as hown. The velocity of the swimmer in still water is same as that of the water (i) In what direction should he try to direct his velocity ? Calculate angle between his velocity anf river velocity. (ii) Find the ratio of the time taken to cross the river in this situation to the minimum time in which he can cross this river.

A swimmer starts to swim from point a to cross a river. He wants to reach point B on the opposite side of the river. The line AB makes an angle 60^(@) with the river flow as shown. The velocity of the swimmer in still water is same as that of the water (i) In what direction should he try to direct his velocity ? Calculate angle between his velocity and river velocity. (ii) Find the ratio of the time taken to cross the river in this situation to the minimum time in which he can cross this river.

The top of two poles of height 16m and 10m are connected by a wire. If the wire makes an angle of 30^(@) with the horizontal, then its length is……….m

An electrician has to repair an electric fault on a pole of height 5m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work (see the given figure). What should be the length of the ladder that she should use which, when inclined at an angle of 60^(@) to teh horizontal, would enable her to reach the required position? Also, how far from the foot of the pole shoudl she place the foot of the ladder? (you may take sqrt3= 1.73 )

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30^(@) with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

On end of a light spring of natural length d and spring constant k is fixed on a rigid wall and the other is attached to a smooth ring of mass m which can slide without friction on a vertical rod fixed at a distance d from the wall. Initially the spring makes an angle of 37^@ with the horizontal. as shown in figure. When the system is released from rest, find the speed of the ring when the spring becomes horizontal. (sin 37^@=3/5) .

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m//s at an angle of 30(@) with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground ? [ g = 10m//s^(2) , sin 30^(@) = (1)/(2) , cos 30^(@) = (sqrt(3))/(2)]