Question

A tower subtends an angle of 30 degree at a point on the same level as its foot. At a second point h metres above the first the angle of depression of the foot of the tower is 60 degree. The height of the tower is ?

Answer 1

A pole subtends an angle of 30° at a

point on the same level as its foot. At a second

point h metres above the first, the depression of

the foot of the pole is 60°. The height of the pole

is :

a) h/2 m b) root3 m c) h/3 m d) h/root3 m

Answer 2

The height of the tower is h / 3 meters.

Given:

The angle of depression of the foot of the tower is 60 degrees and A tower subtends an angle of 30 degrees at a point on the same level as its foot.

To Find:

The height of the tower

Solution:

Let AB be the height of the tower. Tower AB subtends an angle ∠ACB of 30 degrees at a point C on the same level as its foot.

From the figure below

D is h meter above the point C.

In ΔBCD

tan B = CD /CB

⇒ tan 60° =  h /CB

⇒ √3 = h / CB

⇒ CB = h /√3 -------------(1)

In ΔABC

tan C = AB / CB

⇒ tan 30° = AB / (  h /√3)         ( Using (1))

⇒ 1/ √3 = √3 AB / h

⇒ AB =  h / 3

∴The height of the tower  is  h / 3 meters.

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