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
Topic Video
Question
find h
35.00,61.03,35.60,35.71
![**Problem Explanation:**
The image displays a ladder leaning against a building, forming a right triangle. The length of the ladder is 50 feet, and the horizontal distance from the base of the ladder to the building is 35 feet. The problem requires finding the height \( h \), which is the vertical distance from the ground to the point where the ladder touches the building.
**Diagram Details:**
- The ladder forms the hypotenuse of the right triangle.
- The horizontal distance (base of the triangle) is 35 feet.
- The hypotenuse (ladder) is 50 feet.
- The vertical height \( h \) from the ground to the point where the ladder touches the building needs to be determined.
**Multiple Choice Answers:**
- 35.00 ft
- 61.03 ft
- 35.60 ft
- 35.71 ft
**Mathematical Solution:**
To find \( h \), we can use the Pythagorean theorem. For a right triangle:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the horizontal distance (35 ft)
- \( b \) is the vertical height \( h \)
- \( c \) is the length of the ladder (50 ft)
Plugging in the known values:
\[ 35^2 + h^2 = 50^2 \]
\[ 1225 + h^2 = 2500 \]
\[ h^2 = 2500 - 1225 \]
\[ h^2 = 1275 \]
\[ h = \sqrt{1275} \]
\[ h \approx 35.71 \]
Therefore, the correct answer is **35.71 ft**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5608450-3430-44c1-b802-0d7e966fe177%2F8226b563-0920-4536-a78b-db3d64616156%2Futfdy4c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Explanation:**
The image displays a ladder leaning against a building, forming a right triangle. The length of the ladder is 50 feet, and the horizontal distance from the base of the ladder to the building is 35 feet. The problem requires finding the height \( h \), which is the vertical distance from the ground to the point where the ladder touches the building.
**Diagram Details:**
- The ladder forms the hypotenuse of the right triangle.
- The horizontal distance (base of the triangle) is 35 feet.
- The hypotenuse (ladder) is 50 feet.
- The vertical height \( h \) from the ground to the point where the ladder touches the building needs to be determined.
**Multiple Choice Answers:**
- 35.00 ft
- 61.03 ft
- 35.60 ft
- 35.71 ft
**Mathematical Solution:**
To find \( h \), we can use the Pythagorean theorem. For a right triangle:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the horizontal distance (35 ft)
- \( b \) is the vertical height \( h \)
- \( c \) is the length of the ladder (50 ft)
Plugging in the known values:
\[ 35^2 + h^2 = 50^2 \]
\[ 1225 + h^2 = 2500 \]
\[ h^2 = 2500 - 1225 \]
\[ h^2 = 1275 \]
\[ h = \sqrt{1275} \]
\[ h \approx 35.71 \]
Therefore, the correct answer is **35.71 ft**.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education