Question

\angle dac = \angle bad.

what is the length of \overline{ac}?
round to one decimal place.

Explanation:

Step1: Apply the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if \(AD\) is the angle bisector of \(\angle BAC\) (where \(\angle BAD=\angle DAC\)), then \(\frac{AC}{AB}=\frac{CD}{DB}\). Let \(AC = x\). We know \(CD = 2\), \(DB=2.8\), and \(AB = 8.1\).

Step2: Substitute values into the formula

Substituting the values into \(\frac{x}{8.1}=\frac{2}{2.8}\). Cross - multiply to get \(2.8x=2\times8.1\).

Step3: Solve for \(x\)

First, calculate \(2\times8.1 = 16.2\). Then \(x=\frac{16.2}{2.8}\approx5.8\).

Answer:

\(5.8\)