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### Understanding Right Triangles ![Right Triangle](image-link) 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 ![Right Triangle](image-link) 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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 3E
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### Understanding Right Triangles ![Right Triangle](image-link) 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.
Transcribed Image Text:### Understanding Right Triangles ![Right Triangle](image-link) 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.
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