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
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.
To find the distance north and east, we can use basic trigonometry.
First, let's break down the problem. The boat travels 74 miles at a direction of 34 degrees, and then it changes its course to travel 58 miles at a direction of 53 degrees. The total trip is 132 miles.
Now, let's calculate the distances north and east for each part of the trip:
For the first leg of the trip (74 miles at 34 degrees):
To find the distance east:
East = 74 miles * cos(34 degrees)
To find the distance north:
North = 74 miles * sin(34 degrees)
Now, let's calculate the distances north and east for the second leg of the trip (58 miles at 53 degrees):
To find the distance east:
East = 58 miles * cos(53 degrees)
To find the distance north:
North = 58 miles * sin(53 degrees)
Finally, let's sum up the distances north and east for both legs:
Total east = East (leg 1) + East (leg 2)
Total north = North (leg 1) + North (leg 2)
Using a calculator, we can calculate the values:
East (leg 1) ≈ 62.45 miles
North (leg 1) ≈ 47.39 miles
East (leg 2) ≈ 34.90 miles
North (leg 2) ≈ 44.26 miles
Total east = 62.45 miles + 34.90 miles ≈ 97.35 miles
Total north = 47.39 miles + 44.26 miles ≈ 91.65 miles
Therefore, the answer is C: 96.3 miles east and 87.7 miles north.