Answer: 37.14 miles
Step-by-step explanation: To determine the shortest distance from Sierra to Luis, we need to find the hypotenuse of a right triangle formed by their positions relative to E-Burg.
Sierra is 30 miles north of E-Burg, while Luis is 22 miles west of E-Burg. Assuming they are both on a flat plane, the shortest distance between them is the straight line connecting their positions, which forms the hypotenuse of the right triangle.
The base of the triangle is the horizontal distance between Sierra and E-Burg, which is 22 miles. The height of the triangle is the vertical distance between Luis and E-Burg, which is 30 miles.
Using the Pythagorean theorem, we can calculate the hypotenuse (shortest distance) as follows:
hypotenuse^2 = base^2 + height^2
Plugging in the values:
hypotenuse^2 = 22^2 + 30^2
hypotenuse^2 = 484 + 900
hypotenuse^2 = 1384
Taking the square root of both sides:
hypotenuse = √1384
hypotenuse ≈ 37.14 miles
Therefore, the shortest distance from Sierra to Luis is approximately 37.14 miles.