Question

A tower 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 tower is 60°. The height of the tower is 

विकल्प

• \[\frac{h}{2} m\]

• \[\sqrt{3h} m\]

• \[\frac{h}{3} m\]

• \[\frac{h}{\sqrt{3}}m\]

Answer 1

Let AB be the tower and C is a point on the same level as its foot such that ∠ACB = 30°

The given situation can be represented as,

Here D is a point h m above the point C.

In ΔBCD,

`⇒ tan B=(CD)/(CB)`

`⇒ tan 60°=h/(CB)` 

`⇒ sqrt3=h/(CB)` 

`⇒ CB=h/sqrt3`

Again in triangle ABC,

`tan C=(AB)/(CB)`

`⇒ tan30= (AB)/((h/sqrt3))`                  [Using (1)]

`⇒1/sqrt3=AB/((h/sqrt3))`

`⇒ AB=h/3`