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. \\(\bigcirc\\) 2.3 cm \\(\bigcirc\\) 4.0 cm \\(\bigcirc\\) 10.7 cm \\(\bigcirc\\) 18.6 cm

Explanation:

Step1: Find length of $\overline{AC}$

In right $\triangle ABC$, use $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$:
$\sin(30^\circ)=\frac{AC}{AB}$
$AC = AB \times \sin(30^\circ) = 10 \times 0.5 = 5$ cm

Step2: Find length of $\overline{CD}$

In right $\triangle ACD$, use $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$:
$\tan(25^\circ)=\frac{AC}{CD}$
$CD = \frac{AC}{\tan(25^\circ)} = \frac{5}{\tan(25^\circ)} \approx \frac{5}{0.4663} \approx 10.7$ cm

Answer:

10.7 cm (Option C: 10.7 cm)