man drove 13 miles directly east from his home, made a left turn at an intersection, and then aveled 6 miles north to his place of work. If a road was made directly from his home to his plac f work, what would its distance be to the nearest tenth of a mile? The distance would be Number miles.
man drove 13 miles directly east from his home, made a left turn at an intersection, and then aveled 6 miles north to his place of work. If a road was made directly from his home to his plac f work, what would its distance be to the nearest tenth of a mile? The distance would be Number miles.
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,...
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![### Problem Statement on Distance Calculation
A man drove 13 miles directly east from his home, made a left turn at an intersection, and then traveled 6 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
**Calculation:**
To solve this problem, we can consider the path the man drove as two sides of a right-angled triangle. The man's home, the intersection, and his place of work form a triangle where:
- The distance traveled east (13 miles) is one leg of the triangle,
- The distance traveled north (6 miles) is the other leg of the triangle,
- The hypotenuse is the direct distance from his home to his place of work.
We can use the Pythagorean theorem to find the direct distance (hypotenuse):
\[ c^2 = a^2 + b^2 \]
where:
- \( a \) = 13 miles (east distance),
- \( b \) = 6 miles (north distance),
- \( c \) is the hypotenuse (direct distance).
**Detailed Calculation:**
1. Square the lengths of the legs:
\[ a^2 = 13^2 = 169 \]
\[ b^2 = 6^2 = 36 \]
2. Add the squares of the legs:
\[ c^2 = 169 + 36 = 205 \]
3. Take the square root of the sum to find \( c \):
\[ c = \sqrt{205} \approx 14.3 \]
Therefore, the direct distance from the man's home to his place of work is approximately **14.3 miles**.
### Interactive Component
- **Input Field:** The distance would be \[ \_\_\_\_\_\_ \] miles.
- **Buttons:**
- "Submit Assignment"
- "Quit & Save"
- "Back"
- "Question Menu"
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### Educational Focus
Students are encouraged to apply the Pythagorean theorem to solve real-world distance problems involving right-angled triangles. Understanding how to break down a problem into a geometric model and using algebraic methods to find distances is a key skill in both mathematics and practical scenarios.
### Assistance Provided
Students can submit their assignments, save their progress to return later](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3fd69c0-7efa-4645-b075-1464014bad6b%2F744d6a5b-b8b5-4f8b-a0ee-72341352d1a9%2Fc51e0lg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement on Distance Calculation
A man drove 13 miles directly east from his home, made a left turn at an intersection, and then traveled 6 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
**Calculation:**
To solve this problem, we can consider the path the man drove as two sides of a right-angled triangle. The man's home, the intersection, and his place of work form a triangle where:
- The distance traveled east (13 miles) is one leg of the triangle,
- The distance traveled north (6 miles) is the other leg of the triangle,
- The hypotenuse is the direct distance from his home to his place of work.
We can use the Pythagorean theorem to find the direct distance (hypotenuse):
\[ c^2 = a^2 + b^2 \]
where:
- \( a \) = 13 miles (east distance),
- \( b \) = 6 miles (north distance),
- \( c \) is the hypotenuse (direct distance).
**Detailed Calculation:**
1. Square the lengths of the legs:
\[ a^2 = 13^2 = 169 \]
\[ b^2 = 6^2 = 36 \]
2. Add the squares of the legs:
\[ c^2 = 169 + 36 = 205 \]
3. Take the square root of the sum to find \( c \):
\[ c = \sqrt{205} \approx 14.3 \]
Therefore, the direct distance from the man's home to his place of work is approximately **14.3 miles**.
### Interactive Component
- **Input Field:** The distance would be \[ \_\_\_\_\_\_ \] miles.
- **Buttons:**
- "Submit Assignment"
- "Quit & Save"
- "Back"
- "Question Menu"
- "Next"
### Educational Focus
Students are encouraged to apply the Pythagorean theorem to solve real-world distance problems involving right-angled triangles. Understanding how to break down a problem into a geometric model and using algebraic methods to find distances is a key skill in both mathematics and practical scenarios.
### Assistance Provided
Students can submit their assignments, save their progress to return later
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