Asked by Abdulwahab
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?
Answers
Answered by
mathhelper
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°
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°
Answered by
mathhelper
typo:
3rd last line should say:
tan angle = 1121.394/383.022 = 2.92775..
(the rest is correct)
3rd last line should say:
tan angle = 1121.394/383.022 = 2.92775..
(the rest is correct)
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