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

Question

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, 2 : 3, 3 : 1, 3 : 2, 1 : 3

MARKS App · Accepted Answer

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

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