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An aeroplane is flying above a horizonta...

An aeroplane is flying above a horizontal road between the two consecutive kilometer's stones. These stones are on the opposite sides of the aeroplane. The angles of depressionof these stones from the aeroplane are `30^(@)" and "60^(@)`. Find the height of the aeroplane from the road.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt3/4Km`
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From the top of the hill; the angle of depressions of two consecutive kilometre stones due east are found to be 30^(@) and 45^(@) Find the height of the hill.

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Knowledge Check

  • The angle of depression of two consecutive kilometer stones in opposite direction from an aeroplane lying above the horizontal line joining the two stones are respectively 60^(@) and 45^(@) . What is the height of the aeroplane ?

    A
    500 m
    B
    `500sqrt(3)` m
    C
    1500 m
    D
    `500(3-sqrt(3))m`

  • From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be alpha and beta . The height of the aeroplane above the road is

    A
    `(tanalpha+tanbeta)/(tanalphatanbeta)`
    B
    `(tanalpha tanbeta)/(tanalpha+tanbeta)`
    C
    `(cotalphacotbeta)/(cotalpha+cotbeta)`
    D
    None

  • From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be alpha and beta . The height of the aeroplane above the road is

    A
    `(tan alpha + tan beta)/(tan alpha tan beta)`
    B
    `(tan alpha tan beta)/(tan alpha + tan beta)`
    C
    `(cot alpha cot beta)/(cot alpha + cot beta)`
    D
    none of these

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    From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive kilometre-stones on the opposite sides of the aeroplane are observed to be alpha and beta. The height of the aeroplane above the road is

    An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45^(0) and 60^(@). Find the width of the river.

    The angles of elevation of an aeroplane from two places 10 km apart are found to be 60^(@) and 30^(@) respectively. Find the height of the aeroplane.

    An aeroplane at an altitude of 200 m observes the angles od depression of opposite points on the two banks of a river to be 45^(@)and60^(@) . Find the width of the river.

    An aeroplane at an altitude of 200 m observes angles of depression of opposite points on the two banks of the river to be 45^(@) and 60^(@) , find the width of the river.

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