Answer:
b = (5/3)√13
Step-by-step explanation:
The cosine of ∠A is AC/AB = 5/13.
The cosine of half of ∠A is given by the half-angle formula ...
cos(A/2) = √((1 +cos(A))/2) = √((1 + 5/13)/2) = √(9/13) = 3/√13
The length of the segment b is found from ...
cos(A/2) = 5/b . . . . . adjacent side/hypotenuse
b = 5/cos(A/2) = 5/(3/√13)
b = (5/3)√13
