Question

find the length of (overline{ac}). use that length to find the length of (overline{cd}). what is the length of (overline{cd})? round to the nearest tenth. ○ 2.3 cm ○ 4.0 cm ○ 10.7 cm ○ 18.6 cm

Explanation:

Step1: Find length of \( \overline{AC} \)

In right triangle \( ABC \), \( \sin(30^\circ) = \frac{AC}{AB} \). Given \( AB = 10 \) cm, so \( AC = AB \cdot \sin(30^\circ) = 10 \cdot \frac{1}{2} = 5 \) cm.

Step2: Find length of \( \overline{CD} \)

In right triangle \( ACD \), \( \cot(25^\circ) = \frac{CD}{AC} \). So \( CD = AC \cdot \cot(25^\circ) \). \( \cot(25^\circ) \approx 2.1445 \), thus \( CD \approx 5 \cdot 2.1445 \approx 10.7 \) cm.

Answer:

10.7 cm (corresponding to the option "10.7 cm")