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
Related questions
Concept explainers
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
![### Right Triangle ABC
In this diagram, we have a right triangle labeled as ABC. Here are the key features and measurements of the triangle:
- **Vertices**: The triangle has three vertices labeled A, B, and C. The right angle is at vertex B.
- **Sides**:
- **AB**: This is one of the legs of the triangle and is perpendicular to side BC.
- **BC**: This is the other leg of the triangle and is horizontal.
- **AC**: This is the hypotenuse of the triangle, opposite the right angle.
### Measurements:
- **Side BC (Base)**: The length of side BC, which is the horizontal leg of the triangle, is given as 24 units.
- **Side AC (Hypotenuse)**: The length of the hypotenuse AC is given as 25 units.
### Right Angle Identification:
- The right angle is marked at vertex B, denoted by a small square symbol.
This diagram is a classic depiction of a right triangle and can be used to study the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC). For this triangle, the relation can be represented as:
\[ AB^2 + BC^2 = AC^2 \]
Given the lengths, you can verify this as:
\[ AB^2 + 24^2 = 25^2 \]
This is a fundamental concept in geometry and is widely applicable in various fields of study.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60897a88-2068-4dd8-9c40-1650c1de52f4%2F7d9b2af0-b374-45e4-b420-360830e6a626%2Fgqaahlq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Right Triangle ABC
In this diagram, we have a right triangle labeled as ABC. Here are the key features and measurements of the triangle:
- **Vertices**: The triangle has three vertices labeled A, B, and C. The right angle is at vertex B.
- **Sides**:
- **AB**: This is one of the legs of the triangle and is perpendicular to side BC.
- **BC**: This is the other leg of the triangle and is horizontal.
- **AC**: This is the hypotenuse of the triangle, opposite the right angle.
### Measurements:
- **Side BC (Base)**: The length of side BC, which is the horizontal leg of the triangle, is given as 24 units.
- **Side AC (Hypotenuse)**: The length of the hypotenuse AC is given as 25 units.
### Right Angle Identification:
- The right angle is marked at vertex B, denoted by a small square symbol.
This diagram is a classic depiction of a right triangle and can be used to study the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC). For this triangle, the relation can be represented as:
\[ AB^2 + BC^2 = AC^2 \]
Given the lengths, you can verify this as:
\[ AB^2 + 24^2 = 25^2 \]
This is a fundamental concept in geometry and is widely applicable in various fields of study.
Transcribed Image Text:**Question:**
What is the measure of Angle A? (Round to the nearest tenth)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning