The top of a hill observed from the top and bottom of a building of height h is at angles of elevation $${\pi \over 6}$$ and $${\pi \over 3}$$ respectively. What is the height of the hill?

If a flage-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?

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?