What are the components of the vector

[anuman]

I'm studying for an exam and can't seem to get this last practice problem! I've tried many ways but still keep getting the wrong answer. The professor has already given us the correct answer to the problems, but I want to know HOW to do it for the exam! Thanks in advance :)

A boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. A vector from the station to the point where the boat was later found is B = 30.0 km, 15.0° north of east.

12. What are the components of the vector from the point where the distress call was made to the point where the boat was found? In other words, what are the components of vector C = B - A?

x component y component
A)17.3 km, east 35.7 km, south
B)35.7 km, west 17.4 km, north
C)40.6 km, east 51.2 km, south
D)17.3 km, west 51.2 km, south
E)40.6 km, east 35.7 km, north

13. How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector C?
A)65.3 km B)39.7 km C)26.5 km D)54.0 km E)42.5 km

 

[chrisk]

Create a coordinate system with the origin at the Coast Guard Station. Use unit vectors of <x> in the east direction and <y> in the north direction. Then the vectors A and B can be expressed as

A = 45cos(75)<x> + 45sin(75)<y>
B = 30cos(15)<x> + 30sin(15)<y>

Then C = B - A is

C = (30cos(15) - 45cos(75))<x> + (30sin(15) - 45cos(75))<y>

The magnitude of C = sqrt( Cx² + Cy²), where Cx is the magitude of the x component and Cy is the magnitude of the y component of the vector C.