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.

Answer 1

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