A vertical tower stands on a horizontal plane and is surmounted by aflag-staff of height 7 m. From a point on the plane, the angle ofelevation of the bottom of the flag-staff is 30º and that of the top ofthe flag-staff is 45º. Find the height of the tower.
Given:
Height of the flagstaff, h = 7 m
Angle of elevation of the bottom of flagstaff, θ = 30°
Angle of elevation of top of flag staff, ϕ = 45 °
To find: Height of the tower
Solution:
Let BC be the height of the tower and DC be the height of the flag-staff.
In right angle Δ ABC,
AB = BC cot 30°
AB = BC × √ 3 …………………. (i)
In right angled Δ ABD,
AB = BD cot 45°
AB = (BC + CD) cot 45°
AB = (BC + 7) …………………. (ii)
Equating (i) and (ii)
(BC + 7) = BC × √3
BC( √3 - 1) = 7
BC = 7/0.73
= 9.58 m
Therefore the height of the tower is 9.58 m.