Advertisements
Advertisements
प्रश्न
A storm broke a tree and the tree top rested on ground 20 m away from the
base of the tree, making an angle of 60o with the ground. Find the height
of the tree.
उत्तर
AB = Height of the tree
Tree is broken at C
AC = CD ....... (1)
∠ CDB = 60°
BD = 20 m
In right angled Δ CBD,
`tan60° = (CB)/(BD)`
`sqrt3 = (CB)/20`
`CB = 20sqrt3 m.`
`sin60° = (CB)/(CD)`
CD =`sqrt3/2 = (20sqrt3)/(CD)`
`CD = (2 xx 20sqrt3)/sqrt3`
CD = 40 m.
∴ AC = CD = 40 m. ....... (From (1) )
AB = AC + CB
AB = `(40 + 20sqrt3)` m.
∴ height of the tree = `(40 + 20sqrt3)` m.
APPEARS IN
संबंधित प्रश्न
The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the cloud from the surface of water
A tower stands vertically on the ground. From a point on the ground, 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 600. What is the height of the tower?
A TV tower stands vertically on a bank of a river/canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From a point 20 m away this point on the same bank, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the river/canal.
A tree standing on a horizontal plane is leaning towards the east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively α and β. Prove that the height of the top from the ground is `((b - a)tan alpha tan beta)/(tan alpha - tan beta)`
The angle of elevation on the top of a building from the foot of a tower is 30° . The angle of elevation of the top of the tower when seen from the top of the second water is 60° .If the tower is 60m high, find the height of the building.
The angles of depression of the top and bottom of a tower as seen from the top of a 60 `sqrt(3)` m high cliff are 45° and 60° respectively. Find the height of the tower.
Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as 30° and 60°. Find the distance between the two men. (Use\[\sqrt{3} = 1 . 73\])
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find
(i) how far the pole is from the bottom of a tower,
(ii) the height of the pole. (Use \[\sqrt{3} = 1 . 732\])
A person is standing at a distance of 80 m from a church looking at its top. The angle of elevation is of 45°. Find the height of the church.
An observer , 1.7 m tall , is` 20 sqrt3` m away from a tower . The angle of elevation from the eye of an observer to the top of tower is 300 . Find the height of the tower.
The angle of elevation of a cloud from a point h metre above a lake is θ. The angle of depression of its reflection in the lake is 45°. The height of the cloud is
Two poles are 'a' metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is
The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiation control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms
Three villagers A, B and C can see each other using telescope across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate the vertical height between B and C. (tan 20° = 0.3640, `sqrt3` = 1.732)
If two towers of heights h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1: h2 = ____________.
An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is ____________.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are α and β, respectively. Then the height of the tower is ____________.
Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60° and 30°. Find the length of each pillar and the distance of the point on the road from the pillars. (Use `sqrt3` = 1.732)
