Advertisements
Advertisements
प्रश्न
From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x°, where tan `x^circ = 5/2` and the angle of depression of the foot D of the tower is y°, where tan `y^circ = 1/4`. Calculate the height CD of the tower in metres.
उत्तर
Let CD be the height of the tower
And height of window A from the ground = 10 m
In right ΔAEC, we have
`tan x^circ = (CE)/(AE)`
`\implies 5/2 = (CE)/(AE)` ...`(∵ tan x = 5/2)`
∴ `AE = (2CE)/5` ...(i)
In right ΔAED, we have
`tan y^circ = (ED)/(AE)`
`\implies 1/4 = 10/(AE)`
∴ AE = 40
Now substituting the value AE in (i), we get
`2/5 CE = 40`
`\implies CE = (40 xx 5)/2 = 100 m`
∴ Required height of tower
CD = CE + ED
= (100 + 10) m
= 110 m
संबंधित प्रश्न
At a particular time, when the sun’s altitude is 30°, the length of the shadow of a vertical tower is 45 m. Calculate:
- the height of the tower.
- the length of the shadow of the same tower, when the sun’s altitude is:
- 45°
- 60°
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.
A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in a horizontal line through its base. On covering 60 m, the angle of elevation changes to 60°. Find the height of the building correct to the nearest metre.
The distance of the gate of a temple from its base is `sqrt(3)` times it height. Find the angle of elevation of the top of the temple.
Two persons standing on opposite sides of a tower observe the angles of elevation of the top of the tower to be 60° and 50° respectively. Find the distance between them, if the height of the tower is 80m.
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 angle of elevation of a stationary cloud from a point 25m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. What is the height of the cloud above the lake-level?
The angle of elevation of an aeroplane from a point on the ground is 45°. After 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 3000 m, find the speed of the aeroplane.
A man is standing on the deck of a ship, which is 10 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.
An aeroplane is flying horizontally along a straight line at a height of 3000 m from the ground at a speed of 160 m/s. Find the time it would take for the angle of elevation of the plane as seen from a particular point on the ground to change from 60⁰ to 45⁰. Give your answer correct to the nearest second.
