Question

\angle dac = \angle bad.

what is the length of \overline{cd}?
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 \(\frac{CD}{DB}=\frac{AC}{AB}\). Let \(CD = x\), then \(DB=2.7 + x\) (this is incorrect, actually \(DB\) is given as \(2.7\) and \(AC = 5.8\), \(AB=6.2\)). The correct formula from the Angle - Bisector Theorem is \(\frac{CD}{DB}=\frac{AC}{AB}\). Substituting the known values: \(\frac{x}{2.7}=\frac{5.8}{6.2}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\frac{x}{2.7}=\frac{5.8}{6.2}\). We get \(6.2x=5.8\times2.7\). First, calculate \(5.8\times2.7 = 15.66\). Then \(x=\frac{15.66}{6.2}\).

Step3: Calculate the value of \(x\)

\(x=\frac{15.66}{6.2}=2.525806\cdots\)

Answer:

\(2.5\)