If you place a 36-foot ladder against the top of a building and the bottom of the ladder is 32 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.
If you place a 36-foot ladder against the top of a building and the bottom of the ladder is 32 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.
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
Question
![**Problem Statement:**
If you place a 36-foot ladder against the top of a building and the bottom of the ladder is 32 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.
**Solution Steps:**
1. **Identify Components:**
- Ladder Length (Hypotenuse) = 36 feet
- Distance from the building (Base) = 32 feet
- Height of the building (Opposite Side) = ?
2. **Using the Pythagorean Theorem:**
The Pythagorean Theorem applies here:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse.
3. **Substitute Known Values:**
- Hypotenuse \( c = 36 \) feet
- Base \( a = 32 \) feet
4. **Formula Rearrangement:**
Solve for \( b \) (height of the building):
\[ b^2 = c^2 - a^2 \]
5. **Calculation:**
\[ b^2 = 36^2 - 32^2 \]
\[ b^2 = 1296 - 1024 \]
\[ b^2 = 272 \]
6. **Take the Square Root:**
\[ b = \sqrt{272} \]
\[ b \approx 16.5 \]
Therefore, the height of the building is approximately **16.5 feet**.
**Graph/Diagram Explanation:**
1. **Right Triangle Representation:**
- **Hypotenuse (Ladder):** 36 feet
- **Base (Distance from Building to Ladder):** 32 feet
- **Height (Opposite side):** 16.5 feet (calculated)
2. **Interactive Input Field:**
- An answer input field labeled "Answer:"
- A button labeled "Submit Answer" for user interaction
- Below the input field is a status line indicating "attempt 1 out of 2 / problem 1 out of max 1"
**Note:**
There are no additional graphs or diagrams provided in the image. The explanation provided via the steps and illustration of right triangle components should suffice for understanding the calculation and solution process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb59a93f1-c544-43ca-8f46-fbe654f100c7%2Fdf05fa28-2dcb-47a8-bc32-217bf81051cf%2Fvwv3zci_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If you place a 36-foot ladder against the top of a building and the bottom of the ladder is 32 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.
**Solution Steps:**
1. **Identify Components:**
- Ladder Length (Hypotenuse) = 36 feet
- Distance from the building (Base) = 32 feet
- Height of the building (Opposite Side) = ?
2. **Using the Pythagorean Theorem:**
The Pythagorean Theorem applies here:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse.
3. **Substitute Known Values:**
- Hypotenuse \( c = 36 \) feet
- Base \( a = 32 \) feet
4. **Formula Rearrangement:**
Solve for \( b \) (height of the building):
\[ b^2 = c^2 - a^2 \]
5. **Calculation:**
\[ b^2 = 36^2 - 32^2 \]
\[ b^2 = 1296 - 1024 \]
\[ b^2 = 272 \]
6. **Take the Square Root:**
\[ b = \sqrt{272} \]
\[ b \approx 16.5 \]
Therefore, the height of the building is approximately **16.5 feet**.
**Graph/Diagram Explanation:**
1. **Right Triangle Representation:**
- **Hypotenuse (Ladder):** 36 feet
- **Base (Distance from Building to Ladder):** 32 feet
- **Height (Opposite side):** 16.5 feet (calculated)
2. **Interactive Input Field:**
- An answer input field labeled "Answer:"
- A button labeled "Submit Answer" for user interaction
- Below the input field is a status line indicating "attempt 1 out of 2 / problem 1 out of max 1"
**Note:**
There are no additional graphs or diagrams provided in the image. The explanation provided via the steps and illustration of right triangle components should suffice for understanding the calculation and solution process.
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 2 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