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

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

Grade:

1 Answers

shaswat roy
19 Points
9 years ago

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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