A tower subtends an angle α at a point in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is β. Then height of the tower is :

Question

A tower subtends an angle α at a point in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is β. Then height of the tower is : (A) b tan α cot β (B) b cot α tan β (C) b tan α tan β (D) b cot α cot β

Tardigrade Admin · Accepted Answer

Let the height of the tower be h. In triangle A B C, tan α=(h/A B) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2504522bc7794d8cd74447d1b5a250f3-.png" /> ⇒ A B =h cot α ...(i) In Δ A B D, tan β =(b/A B) ⇒ A B =b cot β ...(ii) From Eqs. (i) and (ii) h cot α=b cot β ⇒ h=b tan α cot β

Q. A tower subtends an angle $α$ at a point in the plane of its base and the angle of depression of the foot of the tower at a point $b f t$ just above $A$ is $β$ . Then height of the tower is :

$b tan α cot β$

$b cot α tan β$

$b tan α tan β$

$b cot α cot β$

Let the height of the tower be $h$ .
In $△ A BC$ ,
$tan α = \frac{h}{A B}$

$\Rightarrow A B = h cot α$ ...(i)
In $Δ A B D,$
$tan β = \frac{b}{A B}$
$\Rightarrow A B = b cot β$ ...(ii)
From Eqs. (i) and (ii)
$h cot α = b cot β$
$\Rightarrow h = b tan α cot β$

Q. A tower subtends an angle α at a point in the plane of its base and the angle of depression of the foot of the tower at a point bft just above A is β. Then height of the tower is :

btanαcotβ

bcotαtanβ

btanαtanβ

bcotαcotβ