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?

1. 👍 0
2. 👎 0
3. 👁 548
1. 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

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math,geometry

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle ACB = 39^\circ$. Find $\angle PBC$ in degrees.

2. ### math

Altitudes AD and BE of acute triangle ABC intersect at point H. If angle AHB = 123 degrees and angle BAH = 26 degrees, then what is angle HCA in degrees? Asymptote code below [asy] size(150); defaultpen(linewidth(0.8)); pair B =

3. ### Algebra

Which statement about a right triangle is NOT true? A.) The hypotenuse is the longest side of the triangle. B.) The square of the hypotenuse is equal to the sum of the squares of the other two lengths. C.) The sum of the length of

4. ### maths-urgently needed

In right angled triangle ABC angle B=90 degree and AB= root 34 unit. The coordinates of point B and Care (4,2)and (-1,y) respectively. If area of triangle ABC = 17 sq.units, then find value of y.

1. ### Geometry

In right triangle ABC, ∠A is a right angle and sinC=1517. Triangle A B C with a right angle at A and hypotenuse B C. What is the ratio cos C? Enter your answer as a fraction in simplest form, like this: 42/53

2. ### Trigonometry

(Triangle ABC is scalene) AC is a straight shore line and B is a boat out at sea. Angle A is 60 degrees and Angle C is 45 degrees. Find the shortest distance from the boat to the shore if A and C are 5km apart...I honestly have no

3. ### Math

the right triangle ABC, the altitude from vertex C divides the hypotenuse into two segments, one of length 2 and the other of length 16. Find the perimeter of triangle ABC.

4. ### Maths Constructions

How to construct a Triangle ABC in which base BC=4.8 cm, Angle B=90° and hypotenuse AC=6.2 cm.

1. ### math

1. What is the correct classification for the triangle shown below? A triangle has two angles measuring 68 degrees and 22 degrees. (1 point) acute, scalene acute, isosceles --- right, scalene obtuse, scalene 2. What is the value

2. ### Math

Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)? c = 3.1058 c = 12.4233 c = 44.7846 c = 46.3644 In triangle ABC, find b, to the nearest degree,

3. ### Genius Math

Triangle ABC has AC=BC, angle ACB=96 degrees. D is a point in ABC such that angle DAB=18 degrees and angleDBA=30 degrees. What is the measure in degrees of angle ACD? I got 42 degrees!

4. ### geomerty

The following triangles, Ä ABC and Ä DEF, are congruent. abc 67.38degree 12cm lenght 22.62degree b5cm,l,13cm Find the lengths of all missing sides and measures of all angles for both triangles. Include correct units with each of