If two vertical poles 20 ~m and 80 ~m high stand apart on a horizontal plane, then the height (in m ) of the point of intersection of the lines joining the top of each pole to the foot of other is

Step-by-step solution

We put one pole at origin. B C=80 ~m , O A=20 ~m Line O C and A B intersect at M . To find: Length of M N . Eqn of O C: y= ( 80-0 a-0 ) x y= 80 a x Eqn of A B: y= ( 20-0 0-a )(x-a) y= -20 a (x-a) At M:(1)=(2) aligned & 80 a x= -20 a (x-a) & 80 a x= -20 a x+20 x= a 5 & y= 80 a a 5 =16 aligned