If the angles of elevation of the top of a tower from three collinear points A , B and C on a line leading to the foot of the tower are 30 ° , 45 ° and 60 ° respectively, then the ratio A B : B C , is

Step-by-step solution

Let, the height of the tower = h Let, A B = x ,   B C = y ,   C D = z In ∆ A D E ,   tan ⁡ 30 o =   h x + y + z ⇒ x + y + z = 3 h     . . . i In ∆ B D E ,   tan 45 ° = h y + z ⇒ y + z = h     . . . i i In ∆ C D E ,   tan 60 ° = h z ⇒ z = h 3     . . . i i i From i i   &   i i i ,   y = h 1 -   1 3     . . . i v From i   &   i i ,   x = 3 - 1 h   &#