A spherical balloon of radius r subtends an angle $$\alpha$$ at the eye of an observer, while the angle of elevation of it centre is $$\beta$$. What is the height of the centre of the balloon (neglecting the height of the observer) ?

A ladder 9m long reaches a point 9m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60$$^\circ$$. What is the height of the flagstaff?

The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y. If AB = z, then which one of the following is correct?

Consider the following for the next two (02) items that follow :

A flagstaff 20 m long standing on a pillar 10 m high subtends an angle tan^-1(0.5) at a point P on the ground. Let θ be the angle subtended by the pillar at this point P. 

If x is the distance of P from the bottom of the pillar, then consider the following statements :

1. x can take two values which are in the ratio 1 : 3

2. x can be equal to the height of the flagstaff

Which of the statements given above is/are correct?