Final answer:
To find the distance from Newbery to the airport, we use the Pythagorean theorem on the right-angled triangle formed by Dayton, Newbery, and the airport. Solving for 'x' where 'x' is the distance from Newbery to the airport, we find that 'x' is 24 miles.
Step-by-step explanation:
The student's question involves finding the distance from Newbery to the airport, given that Dayton is 10 miles north of the airport, and Newbery is directly east of the airport, with the distance between Dayton and Newbery being 26 miles. This problem can be visualized as a right-angled triangle, with Dayton and Newbery representing the two points of the triangle that are not the airport, and the distances as sides.
Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, we can calculate the distance from Newbery to the airport. If we let 'x' be the distance from the airport to Newbery, then:
x² + 10² = 26²
x² + 100 = 676
x² = 676 - 100
x² = 576
x = √576
x = 24 miles
Thus, the distance from Newbery to the airport is 24 miles, which corresponds to option (c).