Advertisements
Advertisements
प्रश्न
The angle of elevation of a tower from a point 200 m from its base is θ, when `tan θ = 2/5`. The angle of elevation of this tower from a point 120m from its base is `Φ`. Calculate the height of tower and the value of `Φ`.
उत्तर
Let OT be the tower .
A and B be the two points from where the angle of elevation to the top of the tower is measured.
In ΔAOT,
`"OT"/"OA" = tanθ`
⇒ `"h"/200 = 2/5`
⇒ h = 80 ...(1)
Thus , the height of the tower is 80 m.
In ΔBOT,
`"OT"/"OB" = tanΦ`
⇒ `"h"/120 = tanΦ`
⇒ `80/120 = tanΦ` [Using (1)]
⇒ `2/3 = tanΦ`
From the table , we get `Φ = 34^circ`.
APPEARS IN
संबंधित प्रश्न
The length of the shadow of a tower standing on level plane is found to be 2y metres longer when the sun’s altitude is 30° than when it was 45°. Prove that the height of the tower is `y(sqrt(3) + 1)` metres.
Calculate AB.
A vertical tower stand on 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 α and that of the top of flagstaff is β. Prove that the height of the tower is
`(h tan alpha)/(tan beta - tan alpha)`
The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is `sqrt(ab)` metre.
An aeroplane takes off at angle of `30^circ` with the ground . Find the height of the aeroplane above the ground when it has travelled 386m without changing direction .
A ladder rests against a tree on one side of a street. The foot of the ladder makes an angle of 50° with the ground. When the ladder is turned over to rest against another tree on the other side of the street it makes an angle of 40° with the ground. If the length of the ladder is 60m, find the width of the street.
The angle of elevation of the top of an unfinished tower at a point 150 m from its base is 30°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?
From a point 10 m above the ground , the angle of elevation of the top of a tower is α and the angle of depression is β . If tan α = `5/2` and tan β = `1/4` , calculate the height of the tower to the nearest metre .
An aeroplane when flying at a height of 4km from the ground passes vertically above another aeroplane at an instant when the angles of the elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplanes at that instant.
The string of a kite is 150 m long and it makes an angle of 60° with the horizontal. Find the height of the kite from the ground.
