Question
A boat travels 74 miles on a course with direction 34 degrees and then changes its course to travel 58 miles at 53 degrees. How far north and how far east has the boat traveled on its 132-mile trip?
A 87.7 miles east and 44.3 miles north
B 35.7 miles east and 96.3 miles north
C 96.3 miles east and 87.7 miles north
D none of these
I got 87.7 miles EAST and 96.3 miles NORTH.. I chose D but am afraid that it is C
A 87.7 miles east and 44.3 miles north
B 35.7 miles east and 96.3 miles north
C 96.3 miles east and 87.7 miles north
D none of these
I got 87.7 miles EAST and 96.3 miles NORTH.. I chose D but am afraid that it is C
Answers
C is in fact correct
AC = AB + BC = 74mi[34o] + 58mi[53o]
AC = (74*sin34+58*sin53) + (74*cos34+58*cos53)I
AC = 87.7 + 96.3i. CW from +y-axis.
AC = 96.3 + 87.7i. CCW from +x-axis.
AC = (74*sin34+58*sin53) + (74*cos34+58*cos53)I
AC = 87.7 + 96.3i. CW from +y-axis.
AC = 96.3 + 87.7i. CCW from +x-axis.