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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`
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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 ?

Knowledge Check

  • 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?

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