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CDS Height & Distance Test 339
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CDS Height & Distance Test 339

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  • Question 1/10
    1 / -0
    On a field, there is a vertical pillar with a tower on its top. At a point 14 meters away from the foot of the pillar, the angles of elevation of the top and bottom of the tower are and  respectively. Find the difference of the height of the pillar and the tower.

    Solutions

    In triangle BCD,

    Hence, height of pillar is 14 meters

    In triangle ABC,

    AD = AB – BD =

    Difference of height of pillar and the tower = BD – AD =

    Hence, option d is the correct answer.

  • Question 2/10
    1 / -0
    A ball is dropped from a height 64 m above the ground and every time it hits the ground it rises to a height equal to half of the previous. What is the height attained after it hits the ground for the 16th time?
    Solutions
    Height attained after hitting 16th time = 64 (1 -1/2)16
    = 26-16
    = 2-10
  • Question 3/10
    1 / -0
    What is the angle of elevation of the sun when the shadow of a pole is times the length of the pole?
    Solutions
    tan θ=x/x=1/ = tan 30

    Θ=30 Degree
  • Question 4/10
    1 / -0
    A ladder 25 m long is leaning against a wall which is perpendicular to the level ground. The bottom of the ladder is 7 m from the base of the wall. If the top of the ladder slips down 4 m, how much will the bottom of the ladder slip?
    Solutions
    Let ladder AB comes to position A’B; after slip
    From triangle AOB, OB = = 24m
    Thus, OB’ = 24-4 = 20m
    From triangle B’OA’
    OA’ = = 15m
    Thus, ladder AB slip down on base = AA’ – OA’ = 15 -7 = 8 m
  • Question 5/10
    1 / -0
    What is the angle of elevation of the sun, when the shadow of a pole of height 20 m is ?
    Solutions

    In right angled triangled ABC

    ⇒

    ⇒

    ⇒

  • Question 6/10
    1 / -0
    In a rectangle, the angle between a diagonal and a side is  and the length of this diagonal is 8 cm. The area of the rectangle is
    Solutions

    Let ABCD be the rectangle.

     =

    02c049e3-72f4-43e2-ba5a-88feb348e701.jpg

     

      cm

     

     

      cm

     ar(ABCD) =

     ar(ABCD) =

  • Question 7/10
    1 / -0
    In a right angled triangle ABC, right-angled at B, if cos A =  , then what is sin C equal to ?
    Solutions

    cosA=4/5=AB/AC

    Now in △ABC,(AC)2=(AB)2+(BC)2

    (5)2=(4)2+(BC)2

    (BC)2=25−16=9

    BC = 3,

    Now sinC=AB/AC

    =4/5

  • Question 8/10
    1 / -0
    Two poles of height 7m and 12m stand on a plane ground. If the distance between their feet is 12 m, what is the distance between their top?
    Solutions

    Ab = 7m

    EC = 12m

    BC = 12m

    BC = AD = 12m

    ED = EC – CD = EC – AB = 12 – 7 = 5m

    In ∆AED, (AE)2 = (AD)2 + (ED)2 [by Pythagoras theorem]

    =(12)2 + (5)2

    = 144 + 25 = 169 = (13)2

    AE = 13 m

    the distance between their top is 13m.

  • Question 9/10
    1 / -0
    The angle of elevation of sun when length of shadow of a tree is three times the height of the tree is:
    Solutions


  • Question 10/10
    1 / -0
    When the angle of elevation of sun changes from to , the length of shadow of a tree decreases by meters. What is the height of tree?
    Solutions
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