Solving Vector Direction & Distance Problems - Guam Example

[Lefty9602]

Homework Statement

A ship leaves the island of Guam and sails a distance 300km at an angle 46.0∘ north of west.

In which direction must it now head so that its resultant displacement will be 115km directly east of Guam? (Express your answer as an angle measured south of east)
part B:
How far must it sail so that its resultant displacement will be 115km directly east of Guam?

Homework Equations

The Attempt at a Solution

I drew the problem out and tried to find a right triangle but I can't seem to get one to solve these problems. What do I need to do?

 

[SteamKing]

Homework Statement

A ship leaves the island of Guam and sails a distance 300km at an angle 46.0∘ north of west.

In which direction must it now head so that its resultant displacement will be 115km directly east of Guam? (Express your answer as an angle measured south of east)
part B:
How far must it sail so that its resultant displacement will be 115km directly east of Guam?

Homework Equations

The Attempt at a Solution

I drew the problem out and tried to find a right triangle but I can't seem to get one to solve these problems. What do I need to do?

How do you know you need a right triangle to figure out the solution?

 

[Orodruin]

In your triangle, you know two of the sides and you know the angle between them. This completely specifies the shape of the triangle and you should be able to find any angles by using the laws of sine and cosine. Try to relate the angles of the triangle with the angles that you are looking for.

 

[Lefty9602]

How do you know you need a right triangle to figure out the solution?

I don't know what else to use.

 

[SteamKing]

I don't know what else to use.

There are other kinds of triangles besides right triangles.

Do you know the Law of Sines? The Law of Cosines?

One or both of these may be useful in solving your problem, but you won't know if you stay stuck on trying to use right triangles only.

 

[NascentOxygen]

I drew the problem

Post the figure you drew for the information given.

 

[Lefty9602]

Post the figure you drew for the information given.

Got everything with law of cosines. I got the angle 11.79 to get to 115 meters east of guahm but I don't know how to make it in the south of east direction.

 

[NascentOxygen]

in the south of east direction

Basically, it's asking for the angle of the path expressed relative to a line directly east.