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CAT Practice : Trigonometry

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Height of a flag pole

    Q.16: A flag is hoisted on top of a building of height 7√3 m. A man of height √3 m,standing on the ground, sees the top and bottom of the flag pole at 2 different angles of elevation that are found to be complementary. If the man is standing √135 m away from the building, find the height of the flag pole.
    1. 3√3 m
    2. 1.5√3 m
    3. 2 / √3 m
    4. 6 / √3 m

 

  • Correct Answer
    Choice B. 1.5√3 m

Detailed Solution


Let height of the flag pole PQ be x
Height of building QR = 7√3 m
Height of man AB = √3
Therefore QQ’ = 7√3 – √3 = 6√3

From diagram, tan y° = QQ’/AQ’
Or tan y° = ------- (1)

Also, tan (90 – y)° = PQ’/AQ’
Or tan (90 – y)° =
But tan (90 – y)° = cot y°
Therefore cot y =
or tan y = --------(2)

Equating (1) and (2), we get
=
6√3x + 108 = 135
6√3x = 27
x = 9 / 2√3 or x = 1.5√3


Answer choice (B)

Correct Answer: 1.5√3 m



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