Advertisements
Advertisements
प्रश्न
The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.
विकल्प
True
False
उत्तर
This statement is False.
Explanation:
Case I: Let the height of the tower is h and BC = x m
In ΔABC,
tan 30° = `"AC"/"BC" = "h"/x`
⇒ `1/sqrt(3) = "h"/x` ...(i)
Case II: By condition, the height of the tower is doubled i.e., PR = 2h.
In ΔPQR,
tan θ = `"PR"/"QR" = (2"h")/x`
⇒ tan θ = `2/x xx x/sqrt(3)` ...`[∵ "h" = x/sqrt(3), "from equation (i)"]`
⇒ tan θ = `2/sqrt(3)` = 1.15
∴ θ = tan–1(1.15) < 60°
Hence, the required angle is not doubled.
APPEARS IN
संबंधित प्रश्न
In the following figure, in ΔABC, BC = 1, AC = 2, ∠B = 90°. Find the value of sin θ.
A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60° with the level of the ground. Determine the height of the wall.
The angle of elevation of an aeroplane from a point on the ground is 45°. After a flight of 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 3000 metres, find the speed of the aeroplane.
A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is
60°. Find the length of the string assuming that there is no slack in the string.
Radii of the top and the base of a frustum of a cone are 5 cm and 2 cm respectively. Its height is 9 cm. Find its volume. (π = 3.14)
A flag pole ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find radius of the dome `(sqrt(3) = 1.732)`
The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is
If at some time, the length of the shadow of a tower is `sqrt3` times its height, then the angle of elevation of the sun, at that time is ____________.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower.
