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

Answer:

Let the height of the tower be h.

Let the distance between the foot of the tower and the point till which the man walks 192m be y.

Hence

tanθ=

192+y

h

=

12

5

12h=960+5y ..(i)

tan(ϕ)=

y

h

=

4

3

4h=3y ...(ii)

Substituting in i, we get

9y=960+5y

4y=960

y=240 m

Hence h=

4

3

×240

=180 m