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
Topic Video
Question
![**Pythagorean Theorem (Level 2)**
**Problem Statement:**
Find the length of the third side. If necessary, write in simplest radical form.
**Diagram Explanation:**
A right triangle is depicted on graph paper. One leg of the triangle is labeled with a length of \(8\), and the hypotenuse (the side opposite the right angle) is labeled with a length of \(2\sqrt{41}\).
**Solution:**
Using the Pythagorean Theorem, which states \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs of the triangle and \(c\) is the hypotenuse, we can find the length of the missing side.
Given:
- One leg (\(a\)) = \(8\)
- Hypotenuse (\(c\)) = \(2\sqrt{41}\)
The Pythagorean Theorem provides the relationship:
\[ a^2 + b^2 = c^2 \]
Plugging in the known values:
\[ 8^2 + b^2 = (2\sqrt{41})^2 \]
\[ 64 + b^2 = 4 \cdot 41 \]
\[ 64 + b^2 = 164 \]
Solving for \(b^2\):
\[ b^2 = 164 - 64 \]
\[ b^2 = 100 \]
\[ b = \sqrt{100} \]
\[ b = 10 \]
Therefore, the length of the missing side is 10.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79629784-9084-461f-9ae9-4cf541f3f365%2Fff2a5c54-88aa-4a1b-b4e3-2d0a9b243ca0%2Fva2rhr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Pythagorean Theorem (Level 2)**
**Problem Statement:**
Find the length of the third side. If necessary, write in simplest radical form.
**Diagram Explanation:**
A right triangle is depicted on graph paper. One leg of the triangle is labeled with a length of \(8\), and the hypotenuse (the side opposite the right angle) is labeled with a length of \(2\sqrt{41}\).
**Solution:**
Using the Pythagorean Theorem, which states \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs of the triangle and \(c\) is the hypotenuse, we can find the length of the missing side.
Given:
- One leg (\(a\)) = \(8\)
- Hypotenuse (\(c\)) = \(2\sqrt{41}\)
The Pythagorean Theorem provides the relationship:
\[ a^2 + b^2 = c^2 \]
Plugging in the known values:
\[ 8^2 + b^2 = (2\sqrt{41})^2 \]
\[ 64 + b^2 = 4 \cdot 41 \]
\[ 64 + b^2 = 164 \]
Solving for \(b^2\):
\[ b^2 = 164 - 64 \]
\[ b^2 = 100 \]
\[ b = \sqrt{100} \]
\[ b = 10 \]
Therefore, the length of the missing side is 10.
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 1 images
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