Why Is Theta Used as 120.7 Instead of 59.3 in This Hurricane Tracking Problem?

[yang09]

Homework Statement

The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 59.3◦ north of west with a speed of 38.9 km/h. Exactly 2.89 hours later, the course of the hurricane shifts due north, and its speed slows to 27.8 km/h, as shown.
How far from Grand Bahama is the hurricane 4.42 h after it passes over the island?

The problem is already solved and has the solutions to the problem. It is #3. But what I am not understanding is why they used 120.7 as their theta rather than 59.3

Homework Equations

Magnitude (D) = square root ( Dx^2 + Dy^2)

The Attempt at a Solution

I understand how they did the problem, but can you just explain to me why they used 120.7 as their theta and not 59.3. If they use 120.7 as their theta, wouldn't sin120.7 give you your x-component, not your y-component. And when using cos120.7, wouldn't that give you your y-component, not your x-component.

Homework Statement

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[housemartin]

try with theta = 59.3 and compare your answer with the one in the book. Angle simply depends on coordinates you use, magnitude of displacement is independent of this choice, at least it should be ;]

 

[yang09]

i did try it with theta = 59.3. i got a displacement of 139.4, which is wrong

 

[housemartin]

check it again. If you put theta = 59.3 in equations for delta x and delta y in paper which you gave, then the answer for total displacement is the same as with theta = 120.7

 

[yang09]

Ya, you're right. I just used the wrong numbers. But thanks for the help

 

[satxer]

In a compass plot, the 0 degree point is the rightmost part of the plot. See attached:

http://people.rit.edu/pnveme/pigf/TwoDGraphics/twod_dir_compass.gif