Homework Help is Here – Start Your Trial Now!
Math
Geometry
### Identifying Right Triangles **Tell whether each triangle is a right triangle.** #### Example 13 **Diagram Details:** - The triangle is labeled with three sides: 18, 24, and 30 units. - Side lengths are clearly marked along the edges of the triangle. **Question:** - Is this triangle a right triangle? **Answer Choices:** 1. Yes, the triangle is a right triangle. 2. No, the triangle is NOT a right triangle. **Explanation:** To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true. Here, let's check: \[18^2 + 24^2 = 30^2\] Calculations: \[18^2 = 324\] \[24^2 = 576\] \[30^2 = 900\] Adding the squares of the two shorter sides: \[324 + 576 = 900\] Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.

### Identifying Right Triangles **Tell whether each triangle is a right triangle.** #### Example 13 **Diagram Details:** - The triangle is labeled with three sides: 18, 24, and 30 units. - Side lengths are clearly marked along the edges of the triangle. **Question:** - Is this triangle a right triangle? **Answer Choices:** 1. Yes, the triangle is a right triangle. 2. No, the triangle is NOT a right triangle. **Explanation:** To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true. Here, let's check: \[18^2 + 24^2 = 30^2\] Calculations: \[18^2 = 324\] \[24^2 = 576\] \[30^2 = 900\] Adding the squares of the two shorter sides: \[324 + 576 = 900\] Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.

Elementary Geometry For College Students, 7e
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
See similar textbooks
icon
Related questions
Question
### Identifying Right Triangles **Tell whether each triangle is a right triangle.** #### Example 13 **Diagram Details:** - The triangle is labeled with three sides: 18, 24, and 30 units. - Side lengths are clearly marked along the edges of the triangle. **Question:** - Is this triangle a right triangle? **Answer Choices:** 1. Yes, the triangle is a right triangle. 2. No, the triangle is NOT a right triangle. **Explanation:** To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true. Here, let's check: \[18^2 + 24^2 = 30^2\] Calculations: \[18^2 = 324\] \[24^2 = 576\] \[30^2 = 900\] Adding the squares of the two shorter sides: \[324 + 576 = 900\] Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.
Transcribed Image Text:### Identifying Right Triangles **Tell whether each triangle is a right triangle.** #### Example 13 **Diagram Details:** - The triangle is labeled with three sides: 18, 24, and 30 units. - Side lengths are clearly marked along the edges of the triangle. **Question:** - Is this triangle a right triangle? **Answer Choices:** 1. Yes, the triangle is a right triangle. 2. No, the triangle is NOT a right triangle. **Explanation:** To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true. Here, let's check: \[18^2 + 24^2 = 30^2\] Calculations: \[18^2 = 324\] \[24^2 = 576\] \[30^2 = 900\] Adding the squares of the two shorter sides: \[324 + 576 = 900\] Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS