Question

A vertical tower stands on horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take `sqrt(3)` = 1.73)

Answer 1

According to the question,

AD is a flagstaff and BD is a tower.

In ΔABC,

`tan 45^circ = "AB"/"BC"`

⇒ `1 = (h + 6)/"BC"`

⇒ BC = h + 6   ...(i)

In ΔDBC,

`tan 30^circ = "DB"/"BC"`   ...[From (i)]

⇒ `1/sqrt(3) = h/(h + 6)`

⇒ `hsqrt(3) = h + 6`

⇒ `hsqrt(3) - h = 6`

⇒ `h(sqrt(3) - 1) = 6`

⇒ `h = 6/(sqrt(3) - 1) xx (sqrt(3) + 1)/(sqrt(3) + 1)`

⇒ `h = (6(sqrt(3) + 1))/2`

⇒ `h = 3(sqrt(3) + 1)`

⇒ h = 3(1.73 + 1)

⇒ h = 3 × 2.73

⇒ h = 8.19 m.