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Question

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 metres from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60. After some time, the angle of elevation reduces to 30. Find the distance travelled by the balloon during the interval. 


  1. The required distance travelled by the balloon is 183 m

  2. The required distance travelled by the balloon is 283 m

  3. The required distance travelled by the balloon is 583 m

  4. The required distance travelled by the balloon is 983 m


Solution

The correct option is C

The required distance travelled by the balloon is 583 m


Let AB be the position of the girl and AX be the horizontal ground. Let C and D be the two positions of the balloon.

Draw CLAX,DMAX and BNDM, intersecting CL at P.



Then, CBP=60,DBN=30,AB=PL=NM=1.2 m and CL=DM=88.2 m

CP = 88.2 m - 1.2 m = 87 m

From right ΔBPC, we have

BPCP=cot 60=13BP87 m=13BP=87 m3

BP=87 m3×33=293 m

From right ΔBND, we have

BNDN=cot 30=3BP+PNCP=3

293+CD87 m=3   [PN=CD and DN=CP]

293 m+CD=873 m

CD=873 m293 m=583 m

Hence, the required distance travelled by the balloon is 583 m

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