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 Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter10: Quadratic Equations
Section10.4: Solve Applications Modeled By Quadratic Equations
Problem 160E: A city planner wants to build a bridge across a lake in a park. To find the length of the bridge, he...
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![**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.
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