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. 10 cm 30° 25° b c d 2.3 cm 4.0 cm 10.7 cm 18.6 cm

Explanation:

Step1: Find length of $\overline{AC}$ in right - triangle $ABC$

In right - triangle $ABC$, $\sin B=\frac{AC}{AB}$. Given $AB = 10$ cm and $B = 30^{\circ}$, then $AC=AB\sin B$. So, $AC = 10\times\sin30^{\circ}=10\times\frac{1}{2}=5$ cm.

Step2: Find length of $\overline{CD}$ in right - triangle $ACD$

In right - triangle $ACD$, $\tan D=\frac{AC}{CD}$. We know $AC = 5$ cm and $D = 25^{\circ}$. Then $CD=\frac{AC}{\tan D}=\frac{5}{\tan25^{\circ}}$. Since $\tan25^{\circ}\approx0.4663$, $CD=\frac{5}{0.4663}\approx10.7$ cm.

Answer:

$10.7$ cm