Advertisements
Advertisements
प्रश्न
A ladder of length 6meters makes an angle of 45° with the floor while leaning against one wall of a room. If the fort of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60° with the floor. Find the
distance between two walls of the room.
उत्तर
Let AB and CD be the two opposite walls of the room and the foot of the ladder be fixed at
the point O on the ground.
We have,
AO = CO = 6m,∠AOB = 60° and ∠COD = 45°
In ΔABO,
`cos 60°= (BD)/(AO)`
`⇒1/2 = (BO)/6`
`⇒ BO = 6/2`
⇒ BO = 3m
Also, in ΔCDO,
`cos 45° = (DO)/(CO)`
`⇒1/sqrt(2) = (DO)/6`
`⇒ DO = 6/sqrt(2) xx sqrt(2)/sqrt(2)`
`⇒DO = (6 sqrt(2))/2`
`⇒ Do = 3 sqrt(2) m`
Now, the distance between two walls of the room = BD
=BO+DO
`=3+3sqrt(2) `
`=3(1+sqrt(2))`
=3(1+1.414)
=3(2.414)
=7.242
`~~7.24m`
So, the distant between two walls of the room is 7. 24 m.
APPEARS IN
संबंधित प्रश्न
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.
The Distance of the point (−3, 4) from the x-axis is
When an observer at a distance of 12 m from a tree looks at the top of the tree, the angle of elevation is 60°. What is the height of the tree? `(sqrt 3 = 1.73)`
A man is standing on the deck of a ship, which is 40 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill `(sqrt(3) = 1.732)`
In given figure, the value of AE is ____________.
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top ____________.
The top of a banquet hall has an angle of elevation of 45° from the foot of a transmission tower and the angle of elevation of the topmost point of the tower from the foot of the banquet hall is 60°. If the tower is 60 m high, find the height of the banquet hall in decimals.
Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is ______.
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is ______.
A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is 45°. Find the height of the temple.
