**Problem Statement:**A student drives 15 miles west from home and then 30 miles north to go to work. How much shorter would the trip be if it was possible to drive along a straight line from home to work?**Solution Explanation:**To solve this problem, we can use the Pythagorean theorem to find the straight-line distance (the hypotenuse) from the student’s home to work. The student’s path forms a right triangle with legs of 15 miles and 30 miles.Using the Pythagorean theorem:\[c = \sqrt{a^2 + b^2}\]where:- $ a = 15 $ miles,- $ b = 30 $ miles.Calculating:\[c = \sqrt{15^2 + 30^2} = \sqrt{225 + 900} = \sqrt{1125} = 33.54 \text{ miles (approximately)}\]Therefore, the student travels approximately $ 15 + 30 = 45 $ miles total using the original route. The straight-line distance is approximately $ 33.54 $ miles.**Conclusion:**The straight-line path would save the student about $ 45 - 33.54 = 11.46 $ miles.**Diagrams:**In a hypothetical diagram, the path would be visualized as a right triangle with the westward path (15 miles) on the x-axis and the northward path (30 miles) on the y-axis. The hypotenuse would represent the direct path from home to work.This example demonstrates the application of the Pythagorean theorem to find the shortest distance between two points on a coordinate plane.

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Answered: A student drives 15 miles west from…

A student drives 15 miles west from home and then 30 miles north to go to work. How much shorter would the trip be if it was possible to drive along a straight line from home to work.

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

**Problem Statement:**

A student drives 15 miles west from home and then 30 miles north to go to work. How much shorter would the trip be if it was possible to drive along a straight line from home to work?

**Solution Explanation:**

To solve this problem, we can use the Pythagorean theorem to find the straight-line distance (the hypotenuse) from the student’s home to work. The student’s path forms a right triangle with legs of 15 miles and 30 miles.

Using the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

where:
- $ a = 15 $ miles,
- $ b = 30 $ miles.

Calculating:

\[
c = \sqrt{15^2 + 30^2} = \sqrt{225 + 900} = \sqrt{1125} = 33.54 \text{ miles (approximately)}
\]

Therefore, the student travels approximately $ 15 + 30 = 45 $ miles total using the original route. The straight-line distance is approximately $ 33.54 $ miles.

**Conclusion:**

The straight-line path would save the student about $ 45 - 33.54 = 11.46 $ miles.

**Diagrams:**

In a hypothetical diagram, the path would be visualized as a right triangle with the westward path (15 miles) on the x-axis and the northward path (30 miles) on the y-axis. The hypotenuse would represent the direct path from home to work.

This example demonstrates the application of the Pythagorean theorem to find the shortest distance between two points on a coordinate plane.

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