Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30^ , 45^ and 60^ respectively. The ratio of A B to B C is

Step-by-step solution

By sine law, in A B Q 15^ A B = 30^ B Q B Q= 30^ A B 15^ By sine law, in B C Q gathered 120^ B Q = 15^ B C B Q= B C 120^ 15^ gathered From Eqs. (i) and (ii), we get aligned 30^ A B 15^ &= B C 120^ 15^ A B B C - 120^ 30^ &= 30^ 30^ - 3 / 2 1 / 2 A B: B C &= 3 : 1 aligned