Question

David's house is located 7 miles due south of Airfield A. It is also located 7 miles due East of Airfield B. David needs to fly a direct route from Airfield A to Airfield B to the nearest mile how many miles long will this route be?

Answer 1

To find the direct route from Airfield A to Airfield B, apply the Pythagorean theorem to the isosceles right triangle formed by the airfields and David's house. The direct route distance is approximately 10 miles to the nearest mile.

Step-by-step explanation:

The question involves David needing to fly a direct route from Airfield A to Airfield B. With Airfield A being 7 miles due south of his house and Airfield B being 7 miles due east, we can use the Pythagorean theorem to find the direct distance between the two airfields.

Let's define the positions as follows:

• David's house: origin point
• Airfield A: 7 miles south of the origin (0, -7)
• Airfield B: 7 miles east of the origin (7, 0)

Since the airfields create a right-angled triangle with David's house and the legs are equal, the route from A to B is the hypotenuse of an isosceles right triangle. The length of the hypotenuse (direct route) is calculated by the Pythagorean theorem:

c² = a² + b²

Where c is the distance from A to B:

c² = 7² + 7²

c² = 49 + 49

c² = 98

Therefore, c = √98 ≈ 9.9 miles.

So, the direct route David needs to fly from Airfield A to Airfield B is approximately 10 miles to the nearest mile.