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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!!!!

1 answer

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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