Two men standing on opposite sides of a flag staff measure the angles of the top of the flagstaff as 30∘ and60∘. If the height of the flagstaff is 18m the distance between the men is :
A
24m
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B
24√3m
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C
24√3m
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D
31.2m
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Solution
The correct option is B24√3m Let A and B be the points where the two men standing respectively.
Now let angle of elevation of the top of the flag-staff from A be 60o and that of, from the point B be 30o.
Then from ΔAOC
tan60o=OCOA
⇒tan60o=18OA
⇒OA=6√3.....(1).
And, from ΔOBC
tan30o=OCOB
⇒tan30o=18OB
⇒OA=18√3.....(2).
Thus, the distance between the two men is AB=OA+OB=24√3cm. [Using (1) and (2)]