If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? Use the Pythagorean Theorem to solve the problem. Use a calculator to find square roots, rounding to the nearest tenth as needed. OA. 10.6 mi OB. 5.5 mi OC. 20.0 mi OD, 2.0 mi
If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? Use the Pythagorean Theorem to solve the problem. Use a calculator to find square roots, rounding to the nearest tenth as needed. OA. 10.6 mi OB. 5.5 mi OC. 20.0 mi OD, 2.0 mi
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Solving with the Pythagorean Theorem**
**Problem Statement:**
If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? Use the Pythagorean Theorem to solve the problem. Use a calculator to find square roots, rounding to the nearest tenth as needed.
**Options:**
- A. 10.6 mi
- B. 5.5 mi
- C. 20.0 mi
- D. 2.0 mi
**Explanation:**
When solving this problem, consider the path as two sides of a right triangle, where one side is 16 miles (south) and the other is 12 miles (east). The straight-line distance from the starting point forms the hypotenuse of the triangle. Apply the Pythagorean Theorem to find this distance, which is expressed as:
\[ c = \sqrt{a^2 + b^2} \]
where \( a = 16 \) miles, \( b = 12 \) miles, and \( c \) is the hypotenuse.
Calculate \( c \) as follows:
\[ c = \sqrt{16^2 + 12^2} \]
\[ c = \sqrt{256 + 144} \]
\[ c = \sqrt{400} \]
\[ c = 20 \]
Thus, the correct answer is **C. 20.0 mi**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58402a47-f1ff-47ea-9009-84135bb68162%2F7d929990-0cc9-44fd-8c82-bc7045a0cb52%2F6g0i2mt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Solving with the Pythagorean Theorem**
**Problem Statement:**
If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? Use the Pythagorean Theorem to solve the problem. Use a calculator to find square roots, rounding to the nearest tenth as needed.
**Options:**
- A. 10.6 mi
- B. 5.5 mi
- C. 20.0 mi
- D. 2.0 mi
**Explanation:**
When solving this problem, consider the path as two sides of a right triangle, where one side is 16 miles (south) and the other is 12 miles (east). The straight-line distance from the starting point forms the hypotenuse of the triangle. Apply the Pythagorean Theorem to find this distance, which is expressed as:
\[ c = \sqrt{a^2 + b^2} \]
where \( a = 16 \) miles, \( b = 12 \) miles, and \( c \) is the hypotenuse.
Calculate \( c \) as follows:
\[ c = \sqrt{16^2 + 12^2} \]
\[ c = \sqrt{256 + 144} \]
\[ c = \sqrt{400} \]
\[ c = 20 \]
Thus, the correct answer is **C. 20.0 mi**.
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