Advertisements
Advertisements
Question
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° respectively. If the bridge is at a height of 2.5m from the banks, find the width of the river.
Solution
Let A and B be two points on the banks on the opposite side of the river and P be the point on the bridge at a height of 2.5 m.
Thus, we have:
DP = 2.5, ∠PAD = 30° and ∠PBD = 45°
In the right ΔAPD,we have:
`(DP)/(AD) = tan 30° = 1/sqrt(3)`
`⇒ 2.5 /(AD) = 1/ sqrt(3)`
`⇒ AD = 2.5 sqrt(3) m`
In the right ΔPDB,we have:
`(DP)/(BD) = tan 45° = 1`
`⇒ 2.5/(BD) = 1`
⇒ BD=2.5m
`∴"Width of the river" = AB = ( AD+ BD) =(2.5sqrt(3) + 2.5) = 6.83m`
APPEARS IN
RELATED QUESTIONS
A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. `(sqrt 3=1.73)`
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45. Find the height of the tower PQ and the distance PX. (Use `sqrt3=1.73)`
The altitude of the sun at any instant is 60º. Find the height of the vertical pole that will cast a shadow of 30 m.
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
The shadow of a tower standing on a level ground is found to be 40 m longer when Sun’s altitude is 30° than when it was 60°. Find the height of the tower.
A carpenter makes stools for electricians with a square top of side 0.5 m and at a height of 1.5 m above the ground. Also, each leg is inclined at an angle of 60° to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances.
A flag-staff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.
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 ]
Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?
A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be ____________.
