It is known that when Rt△ABC, ∠ C = 90, AD is the bisector, AD=8, AC=4 and 3, and the length of BC is found.
Solution:
As shown in the figure, cos ∠ CAD = AC/AD = 4 √ 3/8 = 3/2.
∴∠CAD=30
AD is the angular bisector.
∴∠BAC=2∠CAD=60
∴∠B=90 -60 =30
∫tan∠B = AC/BC = 4√3/BC =√3/3
∴BC= 12
For reference!