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Question
A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7 meters. At a point in a plane, the angle of elevation of the bottom and the top of the flagstaff are respectively 30° and 60°. Find the height of the tower.
Solution
Let the height of the tower be x m and distance DC = y m.
∴ AB = height of flagstaff = 7 m
Now in right-angled Δ BCD,
`"BC"/"CD" = tan 30°`
∴ `x/y = 1/sqrt3`
⇒ y = √3x ....(i)
Also, in right angled Δ ACD,
`"AC"/"CD" = tan 60°`
⇒ `(x + 7)/y = sqrt3`
⇒ x + 7 = √3y
⇒ x + 7 = 3(√3 x) ...(from (i))
⇒ x + 7 = 3x
⇒ 2x = 7
⇒ x = `7/2` = 3.5 m
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