Problema Solution
An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location in the sea. It then flies 483 miles from the sea at a bearing of S 55° W to another location. Finally, the aircraft flies straight back from the second location to its base. What is the total distance it flies, rounded to the nearest mile
Answer provided by our tutors
The specification of direction "S 46° E" is taken to mean "flying at an angle 46-degrees east of south" and the direction "S 55° W" is taken to mean "flying at an angle 55-degrees east of south - if this interpretation is incorrect then please provide additional information in future problem statements.
the east-west components of flight are therefore opposite to each other and the plane is flying consistently towards the south
the first 550 miles break down into these vectors:
south: 550 * sine(46) = 395.6368
east: 550 * cosine(46) = 382.0621
the next 483 miles break down into these vectors:
south: 483 * sine(55) = 395.6504
east: -1. * 483 * cosine(55) = -277.037
the resultant vector is then approximately:
south: 396.64 + 395.65 = 792.29
east: 382.06 - 277.04 = 105.019
the remaining distance (required to return to base) is then the combination of the resultant vector:
sqrt(792.29^2 + 105.019^2) = 799.2198
the total distance flown, rounded to the nearest mile, is then:
799 + 550 + 483 = 1832