Question

A pilot flies in a straight path for 90​ minutes. She then makes a course correction, heading 20° to the right of her original course, and flies 100 minutes in the new direction. If she maintains a constant speed of 720​ miles per hour, how far is she from her starting position? Round your answer to the nearest mile.

Answer 1

"To solve this problem, we can use the Law of Cosines. Let's call the distance the pilot travels before the course correction d1 and the distance she travels after the course correction d2. We want to find the distance between her starting position and ending position, which we can call D.

First, let's find d1:

d1 = (720 mph) * (90 min / 60 min) = 1080 miles

Next, let's find d2:

d2 = (720 mph) * (100 min / 60 min) = 1200 miles

Now we can use the Law of Cosines:

D² = d1² + d2² - 2d1d2*cos(20°)

D² = 1080² + 1200² - 210801200*cos(20°)

D ≈ 1169 miles

Therefore, the pilot is approximately 1169 miles from her starting position." (ChatGPT, 2023)