### Understanding Right Triangles  A right triangle is a type of triangle that has one angle equal to 90 degrees. In this diagram, the triangle illustrates several important features of right triangles: 1. **Right Angle**: The triangle has a right angle (90 degrees) located at the bottom left corner. This is denoted by the small square in the corner. 2. **Sides**: - The side opposite the right angle is called the hypotenuse. In this triangle, the hypotenuse is labeled as 20. - The other two sides are referred to as the legs. The vertical leg is labeled as 16, and the horizontal leg is labeled as 12. 3. **Additional Angles**: The other two angles in the triangle add up to 90 degrees. These include: - The angle at the top, opposite the vertical side, which is an acute angle (less than 90 degrees). - The angle at the bottom right, opposite the horizontal side, also an acute angle. This is marked with an arc for distinction. ### Special Property - The Pythagorean Theorem In a right triangle, the lengths of the sides satisfy a special relationship known as the Pythagorean Theorem, which states: \[ a^2 + b^2 = c^2 \] Where: - \( a \) and \( b \) are the lengths of the legs (16 and 12 in our case). - \( c \) is the length of the hypotenuse (20 in our case). ### Example Calculation To demonstrate the Pythagorean Theorem with the given triangle: \[ 16^2 + 12^2 = 20^2 \] \[ 256 + 144 = 400 \] \[ 400 = 400 \] This confirms that our triangle follows the Pythagorean Theorem, and all sides are correctly labeled. ### Practical Applications Right triangles are extensively used in various fields such as construction, navigation, engineering, and physics. Understanding the fundamental properties of right triangles and the Pythagorean Theorem allows us to solve many real-world problems involving distances and measurements.
### Understanding Right Triangles  A right triangle is a type of triangle that has one angle equal to 90 degrees. In this diagram, the triangle illustrates several important features of right triangles: 1. **Right Angle**: The triangle has a right angle (90 degrees) located at the bottom left corner. This is denoted by the small square in the corner. 2. **Sides**: - The side opposite the right angle is called the hypotenuse. In this triangle, the hypotenuse is labeled as 20. - The other two sides are referred to as the legs. The vertical leg is labeled as 16, and the horizontal leg is labeled as 12. 3. **Additional Angles**: The other two angles in the triangle add up to 90 degrees. These include: - The angle at the top, opposite the vertical side, which is an acute angle (less than 90 degrees). - The angle at the bottom right, opposite the horizontal side, also an acute angle. This is marked with an arc for distinction. ### Special Property - The Pythagorean Theorem In a right triangle, the lengths of the sides satisfy a special relationship known as the Pythagorean Theorem, which states: \[ a^2 + b^2 = c^2 \] Where: - \( a \) and \( b \) are the lengths of the legs (16 and 12 in our case). - \( c \) is the length of the hypotenuse (20 in our case). ### Example Calculation To demonstrate the Pythagorean Theorem with the given triangle: \[ 16^2 + 12^2 = 20^2 \] \[ 256 + 144 = 400 \] \[ 400 = 400 \] This confirms that our triangle follows the Pythagorean Theorem, and all sides are correctly labeled. ### Practical Applications Right triangles are extensively used in various fields such as construction, navigation, engineering, and physics. Understanding the fundamental properties of right triangles and the Pythagorean Theorem allows us to solve many real-world problems involving distances and measurements.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
A right triangle is a type of triangle that has one angle equal to 90 degrees. In this diagram, the triangle illustrates several important features of right triangles:
1. **Right Angle**: The triangle has a right angle (90 degrees) located at the bottom left corner. This is denoted by the small square in the corner.
2. **Sides**:
- The side opposite the right angle is called the hypotenuse. In this triangle, the hypotenuse is labeled as 20.
- The other two sides are referred to as the legs. The vertical leg is labeled as 16, and the horizontal leg is labeled as 12.
3. **Additional Angles**: The other two angles in the triangle add up to 90 degrees. These include:
- The angle at the top, opposite the vertical side, which is an acute angle (less than 90 degrees).
- The angle at the bottom right, opposite the horizontal side, also an acute angle. This is marked with an arc for distinction.
### Special Property - The Pythagorean Theorem
In a right triangle, the lengths of the sides satisfy a special relationship known as the Pythagorean Theorem, which states:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the legs (16 and 12 in our case).
- \( c \) is the length of the hypotenuse (20 in our case).
### Example Calculation
To demonstrate the Pythagorean Theorem with the given triangle:
\[ 16^2 + 12^2 = 20^2 \]
\[ 256 + 144 = 400 \]
\[ 400 = 400 \]
This confirms that our triangle follows the Pythagorean Theorem, and all sides are correctly labeled.
### Practical Applications
Right triangles are extensively used in various fields such as construction, navigation, engineering, and physics. Understanding the fundamental properties of right triangles and the Pythagorean Theorem allows us to solve many real-world problems involving distances and measurements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0a863c3-fa8c-48bd-b04e-df2a1854546a%2Fce5283c6-bc06-49ce-8cc8-267372a54286%2F9tk2suo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Right Triangles
A right triangle is a type of triangle that has one angle equal to 90 degrees. In this diagram, the triangle illustrates several important features of right triangles:
1. **Right Angle**: The triangle has a right angle (90 degrees) located at the bottom left corner. This is denoted by the small square in the corner.
2. **Sides**:
- The side opposite the right angle is called the hypotenuse. In this triangle, the hypotenuse is labeled as 20.
- The other two sides are referred to as the legs. The vertical leg is labeled as 16, and the horizontal leg is labeled as 12.
3. **Additional Angles**: The other two angles in the triangle add up to 90 degrees. These include:
- The angle at the top, opposite the vertical side, which is an acute angle (less than 90 degrees).
- The angle at the bottom right, opposite the horizontal side, also an acute angle. This is marked with an arc for distinction.
### Special Property - The Pythagorean Theorem
In a right triangle, the lengths of the sides satisfy a special relationship known as the Pythagorean Theorem, which states:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the lengths of the legs (16 and 12 in our case).
- \( c \) is the length of the hypotenuse (20 in our case).
### Example Calculation
To demonstrate the Pythagorean Theorem with the given triangle:
\[ 16^2 + 12^2 = 20^2 \]
\[ 256 + 144 = 400 \]
\[ 400 = 400 \]
This confirms that our triangle follows the Pythagorean Theorem, and all sides are correctly labeled.
### Practical Applications
Right triangles are extensively used in various fields such as construction, navigation, engineering, and physics. Understanding the fundamental properties of right triangles and the Pythagorean Theorem allows us to solve many real-world problems involving distances and measurements.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education