Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![### Geometry Problem: Measuring Arc Length
**Problem Statement:**
Triangle \(ABC\) is inscribed in circle \(O\) with \( \angle A = 43.5^\circ \). Determine the measure of arc \( \overset{\frown}{AB} \).
**Diagram Description:**
The diagram shows a circle centered at point \( O \) with an inscribed triangle \( ABC \). The vertex \( A \) is positioned on the circle with an angle \( \angle A = 43.5^\circ \). The line segment \( AC \) is a radius of the circle, making \( \angle B \) a right angle.
**Options:**
The solution options for the measure of \( \overset{\frown}{AB} \) are:
- A) \( 46.5^\circ \)
- B) \( 93^\circ \)
- C) \( 87^\circ \)
- D) \( 273^\circ \)
**Explanation of Diagram:**
In the circle, point \( O \) is the center, and \( AC \) is a radius forming the right angle \( \angle ABC \). The central angle \( \angle AOC \), which subtends arc \( AB \), can be determined by doubling \( \angle A \).
In this problem:
- \( \angle A = 43.5^\circ \)
- The measure of the arc \( \overset{\frown}{AB} \) is twice the measure of \( \angle A \):
\[
2 \times 43.5^\circ = 87^\circ
\]
Thus, the correct answer is:
- C) \( 87^\circ \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa242a625-2826-4f00-ad8f-039422d3d327%2F0fbc8d93-50ce-408f-b86a-53885b7100e2%2Fypvgzw8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Measuring Arc Length
**Problem Statement:**
Triangle \(ABC\) is inscribed in circle \(O\) with \( \angle A = 43.5^\circ \). Determine the measure of arc \( \overset{\frown}{AB} \).
**Diagram Description:**
The diagram shows a circle centered at point \( O \) with an inscribed triangle \( ABC \). The vertex \( A \) is positioned on the circle with an angle \( \angle A = 43.5^\circ \). The line segment \( AC \) is a radius of the circle, making \( \angle B \) a right angle.
**Options:**
The solution options for the measure of \( \overset{\frown}{AB} \) are:
- A) \( 46.5^\circ \)
- B) \( 93^\circ \)
- C) \( 87^\circ \)
- D) \( 273^\circ \)
**Explanation of Diagram:**
In the circle, point \( O \) is the center, and \( AC \) is a radius forming the right angle \( \angle ABC \). The central angle \( \angle AOC \), which subtends arc \( AB \), can be determined by doubling \( \angle A \).
In this problem:
- \( \angle A = 43.5^\circ \)
- The measure of the arc \( \overset{\frown}{AB} \) is twice the measure of \( \angle A \):
\[
2 \times 43.5^\circ = 87^\circ
\]
Thus, the correct answer is:
- C) \( 87^\circ \)
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