Advertisements
Advertisements
Question
A tower stands vertically on the ground. From a point on the ground, 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 600. What is the height of the tower?
Solution
Let AC be the ladder of length, hm and C be the points, makes an angle of elevation 60° with the wall and foot of the ladder is 9.5 meters away from the wall.
In a triangle ABC, given that BC = 9.5 m and angle C = 60°
Now we have to find the length of the ladder.
So we use trigonometrically ratios.
In a triangle ABC,
`=> cos C = (BC)/(AC)`
`=> cos 60^@ = 9.5/h`
`=> 1/2 = 9.5/h`
`=> h = 19`
Hence length of ladder is 19 meters
APPEARS IN
RELATED QUESTIONS
If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β, prove that the height of the cloud is
`\frac{h(\tan\alpha +\tan \beta )}{\tan \beta -\tan \alpha }`
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
A kit is flying at a height of 75 metres from the ground level, attached to a string inclined at 60 to the horizontal. Find the length of the string to the nearest metre.
The angle of elevation of a tower from a point on the same level as the foot of the tower is 30°. On advancing 150 metres towards the foot of the tower, the angle of elevation of the tower becomes 60°. Show that the height of the tower is 129.9 metres (Use `sqrt3 = 1.732`)
From a point on a bridge across a river, the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If the bridge is at the height of 30 m from the banks, find the width of the river.
Two men on either side of the cliff 80 m high observe the angles of an elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.
The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y.
The tops of two poles of height 16 m and 10 m are connected by a wire of length lmetres. If the wire makes an angle of 30° with the horizontal, then l =
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.
In the given figure, AB is tower of height 50 m. A man standing on its top, observes two car on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the two cars.
