A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 655 mi/h, how far is she from her starting position?

Looks like a clear-cut case of the cosine law,

with sides 655(1.5) or 982.5 and
655(2) or 1310
miles and an angle of 170° between them

let the third side be x
x^2 = 982.5^ + 1310^2 -2(982.5)(1310)cos170°
= 5216449.127
x = √ 52....
= 2283.95 miles

To find how far the pilot is from her starting position, we can break down her flight into two components: the first leg and the second leg.

First, let's calculate the distance traveled during the first leg of the flight.

The pilot flies for 1 hour and 30 minutes, which is equivalent to 1.5 hours.
Since the pilot maintains a constant speed of 655 mi/h, the distance traveled during the first leg can be computed using the formula:

Distance = Speed × Time

Distance_first_leg = 655 mi/h × 1.5 h
Distance_first_leg = 982.5 miles

Next, let's calculate the distance traveled during the second leg of the flight.

The pilot flies for 2 hours in a new direction which is 10 degrees to the right of her original course.
To find the distance traveled during this leg, we need to calculate the component of the total distance that is perpendicular to her original course.

Using trigonometry, we can determine the distance traveled during this leg by finding the projection of the distance on the line perpendicular to the original course direction.

The angle between the original course and the line perpendicular to it is 10 degrees.
So, the perpendicular distance can be calculated by:

Perpendicular distance = Distance × sin(angle)

Perpendicular_distance = 655 mi/h × 2 h × sin(10°)
Perpendicular_distance ≈ 227.04 miles

Finally, to find the total distance from her starting position, we can use the Pythagorean theorem.

Total distance = √(Distance_first_leg^2 + Perpendicular_distance^2)

Total_distance = √(982.5^2 + 227.04^2)
Total_distance ≈ √(965406.25 + 51589.2416)
Total_distance ≈ √1012995.4916
Total_distance ≈ 1006.47 miles (rounded to two decimal places)

Therefore, the pilot is approximately 1006.47 miles away from her starting position.

To find the distance from the pilot's starting position, we can break the journey into two parts: the original course and the course correction.

1. Original Course:
The pilot flies for 1.5 hours (1 hour 30 minutes) at a speed of 655 miles per hour. Therefore, the distance covered on the original course is:

Distance = Speed x Time = 655 mi/h x 1.5 h = 982.5 miles

2. Course Correction:
The pilot makes a course correction and flies for 2 hours at a speed of 655 miles per hour. Since she is now heading 10 degrees to the right of her original course, the distance covered in this direction is:

Distance = Speed x Time = 655 mi/h x 2 h = 1310 miles

To find the distance from the starting position, we need to find the diagonal of the right triangle formed by these two distances. The original course distance is the perpendicular side, and the course correction distance is the base side of the triangle.

Using the Pythagorean theorem, we can calculate the diagonal distance:

Diagonal Distance^2 = Original Course Distance^2 + Course Correction Distance^2

Diagonal Distance^2 = 982.5^2 + 1310^2

Diagonal Distance^2 = 965,206.25 + 1,716,100

Diagonal Distance^2 = 2,681,306.25

Taking the square root of both sides:

Diagonal Distance = √2,681,306.25

Diagonal Distance ≈ 1637.62 miles

Therefore, the pilot is approximately 1637.62 miles from her starting position.