The triangle is a right angled triangle with the right angle at B.


The simplest way to check it is this:

     =  = (25-24)*(25+24) = 1*49 = 49 =  = .


Let H be the distance under the question. Notice that H is nothing else as the altitude of the triangle ABC drawn from 
the right angle vertex B to the hypotenuse AC.


Then we have two expressions for the triangle area 

    Area =  = .


It gives  H = .     ANSWER