Advertisements
Advertisements
प्रश्न
The vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is
30 and that of the top of the flagstaff 60 . Find the height of the tower
[Use `sqrt(3)` 1.732 ]
उत्तर
Let AB be the tower and BC be the flagstaff,
We have,
BC = 6m, ∠AOB = 30° and ∠AOC - 60°
Let AB = h
In ΔAOB
`tan 30° = (AB)/(OA)`
`⇒ 1/ sqrt(3) = h/( OA)`
` ⇒ OA = h sqrt(3)` ..............(i)
Now in Δ AOC,
` tan 60° = (AC)/(OA)`
`⇒ sqrt(3) = (AB +BC)/ (h sqrt(3))` [ Using (i)]
⇒ 3h = h + 6
⇒ 3h - h = 6
⇒ 2h = 6
`⇒ h= 6/2`
⇒ h = 3m
So, the height of the tower is 3 m.
APPEARS IN
संबंधित प्रश्न
A ladder against a vertical wall makes an angle of 45º with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder
A statue 1.46m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the status is 60 and from the same point, the angle of elevation of the top of the pedestal is 45 . Find the height of the pedestal.
The angle of depression form the top of a tower of a point A on the ground is 30° . On moving a distance of 20 meters from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower to from the point B is 60° . Find the height of the tower and its distance from the point A.
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°
Find the distance between the points (a, b) and (−a, −b).
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun ____________.
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°. If the bridge is at a height of 8 m from the banks, then find the width of the river.
Two poles of heights 25 m and 35 m stand vertically on the ground. The tops of two poles are connected by a wire, which is inclined to the horizontal at an angle of 30°. Find the length of the wire and the distance between the poles.
Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is ______.
The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill?
