Home
Class 10
MATHS
The angle of elevation of the top of a t...

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is `60^(@)` and the angle of elevation of the top of the second tower from the foot of the first tower is `30^(@)`. Find the distance between the two towers and also the height of the other tower.

Text Solution

Verified by Experts

Let AB and CD be two tower.
Given that
`CD=30m, angleCBD=60^(@)" and "angleACB=30^(@)`
In `DeltaABC`,
`tan60^(@)=(CD)/(BC) rArr sqrt3=30/(BC)`
`rArr BC=30/sqrt3=10sqrt3m`
`:. " The distance between two towers "=10sqrt3m`
In `DeltaABC`
`tan30^(@)=(AB)/(BC) rArr 1/sqrt3=(AB)/(10sqrt3) rArr AB=10 m`
`:. " Height of other tower "=10 m`
Promotional Banner

Topper's Solved these Questions

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise|32 Videos

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Revision Exercise (short Answer Questions)|5 Videos

  • REAL NUMBERS

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

  • STATISTICS

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

Similar Questions

Explore conceptually related problems

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60^(@) and the angle of elevation of the top of the second tower from the foot of the first tower is 30^(@) . Find the distance between the two and also the height of the tower.

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60^(@) and the angle of elevation of the top of the second tower from the foot of the first tower is 30^(@). The distance between the two towers is m times the height of the shorter tower. What is m equal to ?

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60^@ and the angle of elevation of the top iof the second tower from the foot of the first tower is 30^@ . The distance between the two towers isntimes the height of the shorter tower. What is nequal to?

The angle of elevation of the top of a tower of height H from the foot of another tower in the same plane is 60^(@) and the angle of elevation of the top of the second tower from the foot of the first tower is 30^(@) . If h is the height of the other tower, then which one of the following is correct?

The angle of elevation of the top of a tower of height H from the foot of another tower in the same plane is 60^(@) and the angle of elevation of the top of the second tower from the foot of the first tower is 30^(@). If is the height of the other tower is h , then which one of the following is correct?

The angle of elevation of the top of a building from the foot of the tower is 30^(@) and the angle of elevation of the top of the tower from the foot of the building is 45^(@) . If the tower is 30 m high, find the height of the building.

The angle of elevation of the top of a building from the foot of the tower is 30^(@) and the angle of elevation of the top of the tower from the foot of the building is If the tower is 50m high,find the height of the building.

The angle of elevation of the top of a building from the foot of tower is 30^(@) and the angle of elevation of the top of the tower from the foot of the building is 60^(@). It the tower is 30m high,then the height of the building is

The angle of elevation of the top of a building from the foot of the tower is 30^(@) and the angle of elevation of the top of tower from the foot of the building is 60^(@) ,If the tower is 50 m high, find the height of the building.

The angle of elevation of the top of a hill from the foot of a tower is 60^(@) and the angle of elevation of the top of the tower from the foot of the hill is 30^(@) . If the tower is 50 m high, then what is the height of the hill?