An aircraft flies due North from an airport. After 800 Kilometers, it then travels on a bearing of 050° for 500 Kilometers, at which point it crosses a village. Calculate the distance and bearing of the village from the airport?

Answer 1

translating the angles to standard math and trig notation
North ----> 90°
bearing of 050 ----> 40°

r = (800cos90,800sin90) + (500cos40,500sin40)
= (0, 800) + (383.022, 321.394)
= (383.022, 1121.394)

|r| = √(383.022^2 + 1121.394^2)
= 1185.00 km
tan angle = 1183.0222/321.394 = 3.681
angle = 71.1°

so your bearing would be 18.9°

Answer 2

typo:
3rd last line should say:

tan angle = 1121.394/383.022 = 2.92775..
(the rest is correct)