Question

solving for side lengths of right triangles. 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. 18.6 cm, 2.3 cm, 4.0 cm, 10.7 cm

Explanation:

Step1: Find length of AC in right - triangle ABC

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

Step2: Find length of CD in right - triangle ACD

In right - triangle ACD, $\tan D=\frac{AC}{CD}$. Given $AC = 5$ 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