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At a point on a level plane a vertical t...

At a point on a level plane a vertical tower subtends an angle `alpha` and a pole of height a meters at the top of the tower subtends an angle `beta`. Show that the height of the tower is a `sin alpha " cosec "beta cos(alpha + beta)`.

Answer

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Knowledge Check

  • At a point on a level plane a tower subtends an angle theta and a flag staff 'a' ft. in length at the top of the tower subtends an angle phi . The height of the tower is

    A
    `(asinthetacosphi)/(cos(theta+phi))`
    B
    `(asinphicos(theta+phi))/(sintheta)`
    C
    `(acos(theta+phi))/(sinthetasinphi)`
    D
    None

  • A tower PQ subtends an angle alpha at a point A on the same level as the foot Q of the tower. It also subtends the same angle alpha at a point B where AB subtends the angle alpha with AP then

    A
    AB = BQ
    B
    BQ = 2AQ
    C
    `(AB)/(BQ) = (1//2) sin alpha`
    D
    `(AB)/(BQ) = (1//2) "cosec" alpha`

  • A tower PQ subtends an angle alpha at a point A on the same level as the foot Q of the tower. It also subtends the same angle alpha at a point B where AB subtends the angle alpha with AP, then

    A
    AB=BQ
    B
    `BQ=2AQ`
    C
    `(AB)/(BQ)=1/2sin alpha`
    D
    `(AB)/(BQ)=1/2 cosec alpha`

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