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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.
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