Trigonometry


  1. The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is









  1. View Hint View Answer Discuss in Forum


    AB = Tower = h metre
    BC = 50 metre
    ∠ ACB = 30°

    ∴ tan 30° =
    AB
    BC

    1
    =
    AB
    350

    ⇒ AB =
    50
    metre
    3

    Correct Option: B


    AB = Tower = h metre
    BC = 50 metre
    ∠ ACB = 30°

    ∴ tan 30° =
    AB
    BC

    1
    =
    AB
    350

    ⇒ AB =
    50
    metre
    3


  1. A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is









  1. View Hint View Answer Discuss in Forum


    AB = Tower = h metre
    CD = 100 metre; BC = 160 metre
    ∠ACB = ∴ ∠ADB = 2θ
    In ∆ ABC,

    tanθ =
    AB
    BC

    ⇒ tanθ =
    h
    .............(i)
    160

    In ∆ ABD,
    tan2θ =
    AB
    BD

    ⇒ tan2θ =
    h
    60

    2tanθ
    =
    h
    1 - tan2θ60

    = 2 ×
    h
    160
    1 -
    h2
    160 × 160

    h
    60

    1=
    1
    801 -
    h2
    60
    160 × 160

    ⇒ 41 -
    h2
    = 3
    160 × 160

    h2
    = 1 -
    3
    =
    1
    160 × 16044

    ⇒ h2 = 6400
    ⇒ h = √6400 = 80 metre

    Correct Option: A


    AB = Tower = h metre
    CD = 100 metre; BC = 160 metre
    ∠ACB = ∴ ∠ADB = 2θ
    In ∆ ABC,

    tanθ =
    AB
    BC

    ⇒ tanθ =
    h
    .............(i)
    160

    In ∆ ABD,
    tan2θ =
    AB
    BD

    ⇒ tan2θ =
    h
    60

    2tanθ
    =
    h
    1 - tan2θ60

    = 2 ×
    h
    160
    1 -
    h2
    160 × 160

    h
    60

    1=
    1
    801 -
    h2
    60
    160 × 160

    ⇒ 41 -
    h2
    = 3
    160 × 160

    h2
    = 1 -
    3
    =
    1
    160 × 16044

    ⇒ h2 = 6400
    ⇒ h = √6400 = 80 metre



  1. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is









  1. View Hint View Answer Discuss in Forum

    Height of tower
    Length of stick

    =
    Length of shadow of tower
    Length of shadow of stick

    h
    =
    40
    128

    ⇒ h =
    40 × 12
    = 60 metre
    8

    Correct Option: B

    Height of tower
    Length of stick

    =
    Length of shadow of tower
    Length of shadow of stick

    h
    =
    40
    128

    ⇒ h =
    40 × 12
    = 60 metre
    8


  1. If the angle of elevation of a balloon from two consecutive kilometre-stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be









  1. View Hint View Answer Discuss in Forum


    AB = Height of balloon = h km
    BD = x km, CD = 1 km
    From ∆ ABD.

    tan 60° =
    AB
    BD

    ⇒ √3 =
    h
    x

    ⇒ x =
    h
    km ......(i)
    3

    From ∆ ABC,
    tan 30° =
    AB
    BC

    1
    =
    h
    3
    h
    + 1
    3

    ⇒ √3 h =
    h
    + 1
    3

    ⇒ √3 h -
    h
    = 1
    3

    3h - h
    = 1
    3

    ⇒ 2h = √3
    ⇒ h =
    3
    km
    2

    Correct Option: A


    AB = Height of balloon = h km
    BD = x km, CD = 1 km
    From ∆ ABD.

    tan 60° =
    AB
    BD

    ⇒ √3 =
    h
    x

    ⇒ x =
    h
    km ......(i)
    3

    From ∆ ABC,
    tan 30° =
    AB
    BC

    1
    =
    h
    3
    h
    + 1
    3

    ⇒ √3 h =
    h
    + 1
    3

    ⇒ √3 h -
    h
    = 1
    3

    3h - h
    = 1
    3

    ⇒ 2h = √3
    ⇒ h =
    3
    km
    2



  1. A kite is flying at a height of 50 metre. If the length of string is 100 metre then the inclination of string to the horizontal ground in degree measure is









  1. View Hint View Answer Discuss in Forum


    AB = Height of kite = 50 metre
    OB = length of thread = 100 metre

    ∴ sin BOA =
    AB
    =
    50
    =
    1
    = sin 30°
    OB1002

    ∴ ∠BOA = 30°

    Correct Option: D


    AB = Height of kite = 50 metre
    OB = length of thread = 100 metre

    ∴ sin BOA =
    AB
    =
    50
    =
    1
    = sin 30°
    OB1002

    ∴ ∠BOA = 30°