A tower subtends angles , 2 and 3 respectively at points A, B and C , all lying on a horizontal line through the foot of the tower, then A B B C is equal to:

Step-by-step solution

In E C D , 3 = h C D C D=h 3 ( i ) In E B D , 2 = h B D B D=h 2 ( ii ) In E A D , = h A D A D=h ( iii ) From Eqs. (ii) and (iii), A D-B D=h -h 2 B=h( - 2 ) ( iv ) From Eqs. (i) and (ii), B D-C D=h 2 -h 3 C=h( 2 - 3 ) ( v ) From Eqs. (iv) and (v), A B B C = h( - 2 ) 2( 2 - 3 ) A B B C = - 2 2 2 2 - 3 3 = (2 - ) 2 (3 -2 ) 2 3 = 3 = 3 -4 ^3 =3-4 ^2 =-3-2(1- 2 )=1+2 2