Question

\angle DAC=\angle BAD∠DAC=∠BADangle, D, A, C, equals, angle, B, A, D. What is the length of \overline{AC} AC start overline, A, C, end overline? Round to one decimal place.

Answer 1

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.

$\frac{\text{AB}}{\text{BD}}=\frac{\text{AC}}{\text{CD}}$

By substituting measures of the given sides,

$\frac{6.8}{3.8}=\frac{\text{AC}}{2.5}$

AC = $\frac{6.8\times 2.5}{3.8}$

AC = 4.473

AC ≈ 4.5 units

Therefore, measure of the missing side AC will be 4.5 units.