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Question
A flagstaff stands on a vertical pole. The angles of elevation of the top and the bottom of the flagstaff from a point on the ground are found to be 60° and 30° respectively. If the height of the pole is 2.5m. Find the height of the flagstaff.
Solution
Let AB be the flagstaff, BC be the pole and D be the point on ground from where elevation angles are measured.
In ΔBCD
`"BC"/"CD" = tan 30^circ`
`"BC"/"CD" = 1/sqrt(3)`
`sqrt(3)"BC" = "CD"` ....(1)
In ΔACD
`("AB + BC")/"CD" = tan 60^circ`
`("AB + BC")/"CD" = sqrt(3)`
`"AB" + 2.5 = "CD"sqrt(3) = 3"BC"` [Using (1)]
`"AB" + 2.5 = 3 xx 2.5`
`"AB" + 2.5 = 7.5`
AB = 5
Thus , the height of the flagstaff is 5 m.
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