For the following right triangle, find the side length x. Round your answer to the nearest hundredth. 8. Continue © 2021 McGraw-Hill Education. All Rights Reserved. Terms of u K DELL
For the following right triangle, find the side length x. Round your answer to the nearest hundredth. 8. Continue © 2021 McGraw-Hill Education. All Rights Reserved. Terms of u K DELL
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
![**Solve for the Side Length in a Right Triangle**
**Problem:**
For the following right triangle, find the side length \( x \). Round your answer to the nearest hundredth.
**Diagram Explanation:**
The diagram shows a right triangle with one leg labeled as 4, the other leg labeled as 8, and the hypotenuse labeled as \( x \). The right angle is indicated by the small square at the vertex of the two legs.
**Steps to Solve:**
1. **Identify the right triangle sides**:
- One leg = 4
- Other leg = 8
- Hypotenuse = \( x \) (unknown)
2. **Apply the Pythagorean Theorem**:
\[
a^2 + b^2 = c^2
\]
Where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse.
3. **Substitute the known values into the Pythagorean Theorem**:
\[
4^2 + 8^2 = x^2
\]
4. **Calculate the squares**:
\[
16 + 64 = x^2
\]
5. **Add the values**:
\[
80 = x^2
\]
6. **Solve for \( x \)**:
\[
x = \sqrt{80} \approx 8.94
\]
7. **Final Answer**:
\[
x \approx 8.94 \text{ (to the nearest hundredth)}
\]
**Next:**
- Enter the value 8.94 in the provided answer box.
- Click "Continue" to proceed to the next question.
*This solution follows the standard method using the Pythagorean Theorem, ensuring accuracy in finding the length of the hypotenuse.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb12218e8-a364-4d7b-9622-abb2418bb64e%2Fa0710029-36a7-4a74-b2d2-e3bd908a34e6%2Ficr3mso_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for the Side Length in a Right Triangle**
**Problem:**
For the following right triangle, find the side length \( x \). Round your answer to the nearest hundredth.
**Diagram Explanation:**
The diagram shows a right triangle with one leg labeled as 4, the other leg labeled as 8, and the hypotenuse labeled as \( x \). The right angle is indicated by the small square at the vertex of the two legs.
**Steps to Solve:**
1. **Identify the right triangle sides**:
- One leg = 4
- Other leg = 8
- Hypotenuse = \( x \) (unknown)
2. **Apply the Pythagorean Theorem**:
\[
a^2 + b^2 = c^2
\]
Where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse.
3. **Substitute the known values into the Pythagorean Theorem**:
\[
4^2 + 8^2 = x^2
\]
4. **Calculate the squares**:
\[
16 + 64 = x^2
\]
5. **Add the values**:
\[
80 = x^2
\]
6. **Solve for \( x \)**:
\[
x = \sqrt{80} \approx 8.94
\]
7. **Final Answer**:
\[
x \approx 8.94 \text{ (to the nearest hundredth)}
\]
**Next:**
- Enter the value 8.94 in the provided answer box.
- Click "Continue" to proceed to the next question.
*This solution follows the standard method using the Pythagorean Theorem, ensuring accuracy in finding the length of the hypotenuse.*
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 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