Using Cosine law,
the distance between pilot's current position and his starting position is 2596 miles.
Cosine law:
The law of cosines can help you find the side lengths of a triangle. The sum of the squares of the remaining side lengths minus the product of twice the remaining side length times the opposite cosine angle.
Let a, b, and c be the sides and A, B, and C
be the corners of the triangle.
By the Law of Cosines (also called the Cosine Rule) says:
c² = a²+ b² − 2ab cos(C)
We are given that the constant speed = 650mph
A pilot flies in a straight path for 1 h 45 min. Thus, time = 1.75 hours
The distance travelled in 1.75 hrs (a) = 1.75 × 650
= 1137.5 miles
The pilot makes a course correction, heading 15 degrees to the right of her original course, and flies 2 h in the new direction.
Angle = 15°
The distance traveled in 2 hrs and 30 minutes (b)
= 650×2.5 = 1625 miles
let the distance between pilot current position and starting position be c miles .
Determining the length of c by using the Cosine law: c² = a²+ b² − 2ab cos(C)
putting all the values into above equation
c² = (1137.5)² + (1625)² - 2×1625(1137.5)Cos (15)
=> c² = 6740459.38
=> c = 2596.23 ~ 2596 miles
Hence, the distance between pilot's current position and starting position is 2596 miles.
To learn more about Cosine law or rule, refer :
https://brainly.com/question/4372174
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