Answer:
B. 254.3 miles
Explanation:
If the plane had to return to the airport making a direct flight, all the 3 distances travelled would make up a triangle as shown in the attachment below.
Let x be the distance to travel back to the airport. This unknown distance (x) can be calculated using the Law of Cosines, which is, a² = b² + c² − 2bc cosA
Where,
a = x
b = 160 mi
c = 150 mi
A = 110.167°
Plug in the above values to solve for x
x² = 160² + 150² - 2(160)(150)*cos(110.167)
x² = 25600 + 22500 - 48000*(-0.345)
x² = 48100 + 16560
x² = 64660
x = √64660
x = 254.28
x ≈ 254.3 miles.