To find how far you are from your starting point, we can use the Pythagorean theorem, since the path you described forms a right triangle with the eastward and northward legs being the two shorter sides.

The formula for the Pythagorean theorem is:

$c^2 = a^2 + b^2$

where:

• $c$ is the hypotenuse (the straight-line distance from the starting point),
• $a$ is the distance traveled east (15 miles),
• $b$ is the distance traveled north (17 miles).

Now, plug in the values:

$c^2 = 15^2 + 17^2$ $c^2 = 225 + 289$ $c^2 = 514$ $c = \sqrt{514} \approx 22.7$

So, the straight-line distance from the starting point is approximately 22.7 miles.

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Would you like further explanation on how to apply the Pythagorean theorem?

Here are 5 related questions for you to consider:

1. How would the result change if the eastward distance were 20 miles instead?
2. What if you were traveling in three dimensions instead of two? How would the Pythagorean theorem change?
3. How do you determine if two sides form a right triangle with the Pythagorean theorem?
4. What is the distance if you travel 10 miles east and 24 miles north?
5. How can you apply the Pythagorean theorem in real-world navigation or map reading?

Tip: To avoid errors, always double-check that you're working with the correct sides (legs) for the Pythagorean theorem—those that are perpendicular to each other!