In the given figure, from the top of a building AB = 60 m hight, the angle of depression of the top and bottom of a vertical lamp post CD are observed to be 30 ° and 60 ° respectively. find :
1) the horizental distance between AB and CD ;
2) the height of the lamp post.
A vertical tower stand on a horizontel plane and is surmounted by a vertical flagstaff of height h metre. At a point on the plane, the angle of elevation of the bottom of the flagstaff is ∝ and at the top of the flagstaff is β . prove that the height of the tower is
`"h tan ∝ "/"tan β - tan ∝"`
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°. Calculate:
(i) the width of the river;
(ii) the height of the tree.
The angle of elevation of the top of a tower from a point on the ground and at a distance of 160 m from its foot, is found to be 60o. Find the height of the tower.
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.
A man on a cliff observes a boat, at an angle of depression 30o, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60o. Assuming that the boat sails at a uniform speed, determine:
(i) how much more time it will take to reach the shore. (ii) the speed of the boat in metre per second, if the height of the cliff is 500 m.