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

tan ⁡ 30 o =   h x + y + z ,   tan ⁡ 45 0 = h y + z ,   tan ⁡ 60 0 = h z ⇒     x + y + z =   3   h   ... (i) y + z = h      ... (ii) z = h 3 ... (iii) from (ii) & (iii) y = h 1 -   1 3 ... (iv) from (i) & (ii) x = 3 - 1 h ... (v) x y =   3 - 1 h h 3 - 1 3 =   3 1