Final answer:
Using the Angle Bisector Theorem, we find that the length of segment AC, given AB = 4.8, BD = 4, and DC = 2.3, is 2.76 units. After rounding, this length is approximately 2.8 units.
Step-by-step explanation:
To find the length of segment AC, we first note that AD is the angle bisector of angle BAC. Given that AB = 4.8, BD = 4, and DC = 2.3, we can use the Angle Bisector Theorem to solve for AC. The theorem states that the ratio of the lengths of the two segments on one side of the bisector is equal to the ratio of the lengths of the two corresponding segments on the other side of the bisector.
In this case, we have the following:
- AB / BD = AC / DC
- 4.8 / 4 = AC / 2.3
To find AC, we solve for AC by cross-multiplying:
- 4.8 * 2.3 = 4 * AC
- 11.04 = 4 * AC
- AC = 11.04 / 4
- AC = 2.76
After rounding to the nearest tenth, the length of segment AC is 2.8 units.