Final answer:
The total distance for the two legs of the trip is approximately 640 miles, after accounting for a change in course by 20 degrees to the right and flying at a constant speed of 720 miles per hour for given times.
Step-by-step explanation:
The question involves solving a problem by calculating the total distance a pilot is from the starting point after flying two legs in a straight path at different angles. We use trigonometry and vector addition concepts to solve the problem.
The pilot flies in a straight path for 115 minutes at a speed of 720 miles per hour. First, we need to calculate the distance flown in the first leg by multiplying the time by the speed:
- Distance = Speed × Time
- Distance = 720 miles/hour × 115/60 hours (since 1 hour = 60 minutes)
- Distance = 1380 miles (First leg)
Next, the pilot changes course by 20° to the right and flies for 135 minutes at the same speed. Calculating the distance for the second leg:
- Distance = Speed × Time
- Distance = 720 miles/hour × 135/60 hours
- Distance = 1620 miles (Second leg)
To find the total distance from the starting position, we use the law of cosines because we have a non-right-angled triangle:
- D² = A² + B² - 2ABcos(θ)
- Where D is the total distance from the start, A and B are the distances of the first and second leg, and θ is the angle between them (which is 20°).
- D = √(1380² + 1620² - 2*1380*1620*cos(20°))
- D ≈ 640.5 miles (after rounding to the nearest mile)
The pilot is approximately 640 miles from the starting position after completing the second leg of the trip.