Solution:
Given: A right triangle ABC in which , ∠C = 90°, AC = 5 ft, AB = 13 ft
By using pythagoras theorem, In Δ AC B,
AC² + CB²= AB²
5²+ CB²= AB²
25 + CB²= 13²
CB²= 169 -25
CB²= 144
CB=√144
CB= 12 ft
Let line from vertex A intersects side BC at M that is AM is median.
BM =
In Triangle ACM
AC² + CM²=AM² [By pythagoras theorem]
5² + 6² = AM²
25 + 36= AM²
AM = √61
Length of median = √61 ft
Let AQ be the angle bisector of ∠A.
By Angle bisector theorem
Now In Δ ACQ
AQ²= AC² + CQ² [By pythagoras theorem]
Length of the angle bisector of angle ∠A= AQ =8.34 ft(approx)