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PLEASE HELP!!!!! (Right Triangle Question)

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Point N is on hypotenuse BC of triangle ABC such than angle CAN is 45 degrees.
If AC=8 and AB=6, find AN.


I did Pythagorean Theorem for triangle ABC, and hypotenuse BC will be 10.
I don't know how to continue from there. Oh, I'm also unsure about this, but if angle CAN is 45 degrees, will segment AN be a perpendicular bisector of right angle BAC?
Please help me solve this problem. THANK YOU VERY MUCH!!!!

  • PLEASE HELP!!!!! (Right Triangle Question) -

    Take a look at the Angle Bisector Theorem.

    AN bisects the 90° angle CAB.

    So,

    CN/NB = CA/AB = 8/6

    So, since CB = 10

    CN = 8/14 * 10 = 40/7

    (40/7)^2 + AN^2 = 64
    AN = √(64 - 1600/49) = √(1536/49) = 5.6

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