the acute angle between the medians drawn from the acute angles of an isosceles right angled triangle?

let the vertices of the triangle be O,A,B. where AB is the hypotenuse. [notation:bold letters implies vector]

let midpoint of OA be E and mid point of OB be D.

if you draw the figure, it will be clear that  OE + EB = OB ;  EB = OB - OE  ; OE=(1/2)OA; EB= OB - (1/2)OA

and OA + AD = OD; OD=(1/2)OB;   AD = (1/2)OB - OA

now you simply do, EB.AD and remember |OB| = |OA|

answer comes out to be 37degrees.