1) in triangle ABC, AD is the angle bisector of < A. If BD = 5, CD = 6 and AB = 8, find AC.
check out the angle bisector theorem.
To solve this problem, we can use the Angle Bisector Theorem, which states that in a triangle, if a ray bisects an angle, it divides the opposite side into two segments that are proportional to the lengths of the other two sides.
In triangle ABC, we have AD as the angle bisector of angle A. Given that BD = 5, CD = 6, and AB = 8, we want to find the length of AC.
According to the Angle Bisector Theorem, we have:
AB/BD = AC/CD
Substituting the given values, we have:
8/5 = AC/6
Cross-multiplying, we get:
8 * 6 = 5 * AC
48 = 5AC
Dividing both sides by 5, we find:
AC = 48/5 = 9.6
Therefore, the length of AC is 9.6 units.