Question

The angle of elevation of a tower from a point on the same level as the foot of the tower is 30.,on advancing 150m towards the foot of the tower the angle of elevation of the tower becomes 60. , find the height of the tower {use root 3=1.732}

Answer 1

Use trigonometric ratios in ΔABD,
tan 60° = $\frac{h}{a}$
h = √3a ---(i)
Similarly using trigonometric ratios in ΔABC,
tan 30° = $\frac{h}{a+150}$
√3h = 150 + a ---(ii)
Using equation (i) in equation (ii)
a = 75 ---(iii)
Put the value of a in equation (i) to get the value of h,
h = 75√3
   = 75(1.732)
   = 129.9 m
∴ the height of the tower is 129.9 m