Answer:
AC = 4.5 units
Step-by-step explanation:
In the given triangle ABC,
Segment AD is the angle bisector of ∠BAC.
m∠CAD = m∠BAD = θ
By applying angle bisector theorem in ΔABC,
An angle bisector of the interior angle in a triangle divides the opposite side into segments that are proportional to the other two sides.
[tex]\frac{\text{AB}}{\text{BD}}=\frac{\text{AC}}{\text{CD}}[/tex]
By substituting measures of the given sides,
[tex]\frac{6.8}{3.8}=\frac{\text{AC}}{2.5}[/tex]
AC = [tex]\frac{6.8\times 2.5}{3.8}[/tex]
AC = 4.473
AC ≈ 4.5 units
Therefore, measure of the missing side AC will be 4.5 units.
