Question

from a point on the ground the angle of elevation of the top of a tower is observed to be 60degree . From a point 40m vertically above first point of observation the angle of elevation of the top of the tower is 30degree.Find the height of the tower and as horizontal distance from the point of observation

Answer 1

20√3 will be the answer

Answer 2

Answer:

Height of the tower = 60 m

Horizontal distance from the point of observation = 20√3 m

Step-by-step explanation:

The responsible figure is attached to the answer.

Let the height of the tower (BC) be h and the horizontal distance between the tower and the point of observation (AB) be d.

AB = DE = d

AD = BE = 40

∴ CE = h - 40

In ΔABC,

tan 60 = BC / AB

√3 = h / d

d = h / √3          →          (1)

In ΔCDE,

tan 30 = CE / DE

1 / √3 = (h - 40) / d

d = (h - 40)√3          →          (2)

By substituting (1) and (2),

h / √3 = (h - 40)√3

h = (h - 40)3

h = 3h - 120

3h - h = 120

2h = 120

h = 120 / 2

h = 60

∴ Height of the tower is 60 m.

From (1),

d = h / √3

d = 60 / √3

d = 20√3

∴ The horizontal distance is 20√3 ≈ 34.64 m.

Thank you. ;-))

#adithyasajeevan