To find the distance Adam would have to travel for each option, we can use the Law of Cosines.
For the direct flight from B to A:
Side a = 461.1 miles
Angle A = 60.1 degrees
Angle B = 90 degrees (since it is a right angle)
Using the Law of Cosines:
b^2 = a^2 + c^2 - 2accosA
b^2 = 461.1^2 + c^2 - 2(461.1)(c)cos(60.1)
b^2 = 212,409 + c^2 - 461.1c(0.5)
b^2 = 212,409 + c^2 - 230.55c
For the connecting flight from B to C to A:
Let x be the distance from B to C and y be the distance from C to A.
Using the Law of Cosines for B to C:
x^2 = 461.1^2 + c^2 - 2(461.1)(c)cos(29.8)
x^2 = 212,409 + c^2 - 461.1c(0.875)
x^2 = 212,409 + c^2 - 402.196c
Using the Law of Cosines for C to A:
y^2 = x^2 + 461.1^2 - 2(x)(461.1)cos(78.6)
y^2 = x^2 + 212,409 - 461.1x(0.44)
y^2 = x^2 + 212,409 - 202.764x
Adding x and y for the total distance for the connecting flight:
Total distance = x + y
Total distance = sqrt(x^2) + sqrt(y^2)
Total distance = sqrt(212,409 + c^2 - 402.196c) + sqrt(x^2 + 212,409 - 202.764x)
The difference in frequent flyer miles between the direct flight and the connecting flight would be the total distance for the connecting flight - 461.1 miles.
Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance of about 461.1 miles. A second flight option flies first to city C and then connects to A. The bearing from B to C is N29.8 degrees East, and the bearing from B to A is N60.1 degrees East. The bearing from A to B is S60.1 degrees West, and the bearing from A to C is N78.6 degrees West. How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight?
1 answer
1 answer