Home
Class 12
MATHS
The angle of elevation of the top of a t...

The angle of elevation of the top of a tower a point A due south of it is `30^@` and from a point B due west of it is `45^@` .If the height of the tower is 100 meters ,then find the distance AB.

A

400

B

50

C

100

D

200

Text Solution

Verified by Experts

The correct Answer is:
D
In the following figure OP is the tower .

Op= 100 m
In right angled triangle :POA ,
`tan 30 ^@ = 100 /(OA)`
`therefore OA= 100 cot 30 ^@ = 100 sqrt(3)`
In right angled triangle POB,
`tan 45 ^@=(100)/(OB)`
`therefore OB = 100 cot 45 ^@= 100`
In right angled triangle AOB, using Pythagoras theorem ,we get
`AB^2=OA^2+ OB^2`
`= 3xx 100 ^2+100^2`
`=4xx 100^2`
`therefore AB = 2 xx 100 = 200 m `
Promotional Banner

Topper's Solved these Questions

  • HIGHT AND DISTANCE

    CENGAGE|Exercise Exercise|18 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

Similar Questions

Explore conceptually related problems

the angle of elevation of the top of a tower at a point on the ground 50m away from the foot of the tower is 45^(@) . Then the height of the tower ( in meters ) is ………. .

The angle elevation of the top of a tower from a point C on the ground. Which is 30 m away from the foot of the tower is 30^(@) . Find the height of the tower.

The angle of elevation of the top of a tower from a point O on the ground, qhich is 450 m away from the foot of the tower, is 40^(@) . Find the height of the tower.

The angle of elevation of the top of a hill at a point on the ground 130 m away from the foot of the tower is 45^(@) . Then the height of the tower ( in meter ) is .........

From the top of a building, the angle of elevation of the top of a cell tower is 60^(@) and the angle of depression to its foot is 45^(@) . If distance of the building from the tower is 7m, then find the height ofthe tower.

If the angle of elevation of the top of a tower at a distance 500 metres from its foot is 30^@ then the height of the tower is

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away the foot of a tower of height 10sqrt(3) m.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m, find the height of the tower from the base of the tower and in the same straight line with it are complementary.