Asked by My Name Is Bob
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!!!!
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!!!!
Answers
Answered by
Steve
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
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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