Chapter 9.1, Problem 14WE

To determine

To calculate: the length of $\overline{AB}$.

Answer to Problem 14WE

  $12$ cm.

Explanation of Solution

Given information: For each exercise draw $\odot O$ with radius 12 cm. Then draw radii $\overline{OA}$ and $\overline{OB}$ to form an angle with the measure named. $m\angle AOB=60°$ .

Calculation:

  

Since, from the figure, $AO=OB=12\text{ cm}$ , then $\angle A=\angle B$ .

Now, $\angle A+\angle B+\angle O=180°$ ,

  $\Rightarrow 2\angle A+60°=180°,$

  $\Rightarrow \angle A=60°$ , and $\angle B=60°$ .

Thus, the triangle is isosceles tringle.

Hence, the length of $\overline{AB}=\overline{OA}=\overline{OB}=12$ cm.