Question

From a point in the cricket ground, the angle of elevation of a vertical tower is found to be theta at a distance of 200 meters from the tower. On walking 125 meters towards the tower, the angle of elevation becomes 2 theta. Find the height of the tower.

Answer 1

here it is take the height of the tower to be h apply the formula for tan2theta

Answer 2

Answer:

10 m

Step-by-step explanation:

Refer the attached figure

BD = 200 m

CD = 125 m

BC = 200-125 = 75 m

In ΔABD

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan \theta = \frac{AB}{BD}$

$Tan \theta = \frac{AB}{200}$

In ΔABC

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 2\theta = \frac{AB}{BC}$

$75 Tan 2\theta = AB$

$75 (\frac{2 tan \theta}{1-tan^2 \theta})= AB$

Using A

$75 (\frac{2(\frac{AB}{200}) }{1-(\frac{AB}{200})^2)}= AB$

AB = 10 m

Hence the height of tower is 10 m