Advertisements
Advertisements
प्रश्न
From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag-staff from P is 45°. Find the length of the flag-staff and the distance of the building from the point P. (Take `sqrt3` = 1.732)
उत्तर
Let AB be the flag of length hm on the building BC.
We assume that BC = 10, ∠APC = 45°, ∠BPC = 30°
Now we have to find height of flag-staff and distance of the point P from the building
The corresponding figure is as follows
In a triangle BPC,
`=> tan "P" = ("BC")/("CP")`
`=> tan 30^@ = ("BC")/("CP")`
`=> "CP"="BC"/tan30^@`
`=> 10/(1/sqrt3)`
`= 10sqrt3` m
Again in a triangle ACP
`=> tan "P" = ("AC")/"CP"`
`=> 1 = ("AC")/"CP"`
`=>` AC = CP = 10`sqrt3` m
`=>` AB + BC = CP
`=>` x = 10 = 10`sqrt3`
`=> x = 10sqrt3-10`
`=>10(sqrt3-1)`
= 10 × 0.73
h = 7.32
Hence the length is 17.32 m and distance is 7.32 m
APPEARS IN
संबंधित प्रश्न
From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30º. The angle of elevation of the top of a water tank (on the top of the tower) is 45º. Find the (i) height of the tower (ii) the depth of the tank.
A contractor 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 1.5 m, and is inclined at an angle of 30° to the ground, where as for the elder children, she wants to have a steep side at a height of 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
A person observed the angle of elevation of the top of a tower as 30°. He walked 50 m towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as 60°. Find the height of the tower.
The horizontal distance between two towers is 60 meters. The angle of depression of the top of the first tower when seen from the top of the second tower is 30° . If the height of the second tower is 90 meters. Find the height of the first tower.
If the height of a vertical pole is 3–√3 times the length of its shadow on the ground, then the angle of elevation of the Sun at that time is
(A) 30°
(B) 60°
(C) 45°
(D) 75°
A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree.
A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.
From a point on the ground, 20 m away from the foot of a vertical tower, the angle elevation of the top of the tower is 60°, What is the height of the tower?
An observer, 1.5 m tall, is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer.
The angle of elevation of the top of a vertical tower from a point A, due east of it is 45°. The angle of elevation of the top of the same tower from a point B, due south of A is 30°. If the distance between A and B is `54sqrt(2)` m, then the height of the tower (in metres), is ______.
