Answer:
Town C is approximately 58.356 kilometers from town A.
Step-by-step explanation:
According to the statement, we understand that tourist travels from town A to town B (50 kilometers) at a direction of 80º west of north and from town B to town C (40 kilometers) at a direction of 20º east of north. Vectorially speaking, the resultant from town A to town C is described by the following formula:
[tex]\vec r = (50\,km)\cdot (-\sin80^{\circ},\cos 80^{\circ})+(40\,km)\cdot (\sin 20^{\circ}, \cos 20^{\circ})[/tex]
[tex]\vec r = (-35.560,46.270)\,[km][/tex]
The distance from town A to town C is the magnitude of vector reported above, which is now calculated by Pythagorean Theorem:
[tex]\|\vec r\| = \sqrt{(-35.560\,km)^{2}+(46.270\,km)^{2}}[/tex]
[tex]\|\vec r\| \approx 58.356\,km[/tex]
Town C is approximately 58.356 kilometers from town A.
