Final answer:
The pilot is calculated to be a certain distance from her starting position after flying two legs of her journey, one straight and one at a 20° course correction, both at a constant speed of 720 mph. Using vector addition, trigonometry, and the Pythagorean theorem, we determine the final straight-line distance from her starting point.
Step-by-step explanation:
The question involves determining the distance between a pilot's starting point and her position after flying two legs of a journey at a constant speed but with a change in direction. To solve this problem, we use vector addition and trigonometry. The pilot first flies 115 minutes at 720 miles per hour and then changes course by 20° to the right and flies for another 135 minutes at the same speed.
First, we find the distance covered in each leg of the journey: Distance = Speed × Time. The distances are 115 minutes/60 (to convert to hours) × 720 mph = 1380 miles for the first leg, and 135 minutes/60 × 720 mph = 1620 miles for the second leg.
Next, we create a right-angled triangle with these distances as the adjacent (first leg) and the hypotenuse (second leg) after the course correction. Using cosine for the adjacent leg, we find the opposite leg of the triangle and use the Pythagorean theorem to find the straight-line distance from the starting point.
Let x represent the opposite leg's distance. Then we have:
cos(20°) = 1380/1620
x = 1620 sin(20°)
Now, applying the Pythagorean theorem gives us:
Distance from start (R) = √(1380^2 + x^2).
Calculating these values with the appropriate trigonometric functions and rounding to the nearest mile, we get the total distance R that the pilot is from her starting position.