Chapter 9: Q15. (page 331)

For each exercise draw $⊙ O$ with radius $12$ . Then draw radii $\bar{O A}$ and to $\bar{O B}$ form an angle with the measure named. Find the length of $\bar{A B}$ .
d. $m ∠ A O B = 120 °$

Short Answer

Expert verified

$A B = 20.78$ .

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Isosceles triangle concept. We also use sine formula.

Step 3. Find value.

Since from the figure,

$\begin{matrix} A O = O B \\ A O = 12 \\ O B = 12 \\ ∠ A = ∠ B \end{matrix}$

In role="math" localid="1648892994173" $Δ A O B$ , a isosceles triangle.

$\begin{matrix} ∠ A + ∠ B + ∠ O = 180^{\circ} \\ 2 ∠ A + 120^{\circ} = 180^{\circ} \\ ∠ A = 30^{\circ} \end{matrix}$

So, $∠ B = 30 °$

Now, by sine formula:

$\begin{matrix} \frac{A O}{\sin B} = \frac{A B}{\sin O} \\ \frac{12}{\sin 30^{\circ}} = \frac{A B}{\sin 120^{\circ}} \\ A B = 20.78 \end{matrix}$

Therefore, this length of $A B = 20.78$ .

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For each exercise draw $⊙ O$ with radius $12$ . Then draw radii $\bar{O A}$ and to $\bar{O B}$ form an angle with the measure named. Find the length of $\bar{A B}$ .
d. $m ∠ A O B = 120 °$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Find value.

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For each exercise draw ⊙O with radius 12. Then draw radii OA¯ and to OB¯ form an angle with the measure named. Find the length of AB¯.d. m∠AOB=120°

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Find value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Calculus

Statistics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For each exercise draw $⊙ O$ with radius $12$ . Then draw radii $\bar{O A}$ and to $\bar{O B}$ form an angle with the measure named. Find the length of $\bar{A B}$ .
d. $m ∠ A O B = 120 °$