How to Calculate the Angle for a Boat Crossing a River with a Current?

[bajangal1]

Homework Statement

A boat that can travel at 4.0km/h in still water crosses a river with a current of 2.0 km/h. At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the river?

Homework Equations

No equations were given but it seems like a simple trig problem, just can't get the right answer

The Attempt at a Solution

My first attempt i used inverse tan theta (4/2) and got an angle of 63
My second attempt i used inverse cos theta (2/4) and got an angle of 60

the actual answer is 30. Either there is a very big step I'm missing or I've drawn something horribly wrong.

 

[gneill]

Homework Statement

A boat that can travel at 4.0km/h in still water crosses a river with a current of 2.0 km/h. At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the river?

Homework Equations

No equations were given but it seems like a simple trig problem, just can't get the right answer

The Attempt at a Solution

My first attempt i used inverse tan theta (4/2) and got an angle of 63
My second attempt i used inverse cos theta (2/4) and got an angle of 60

the actual answer is 30. Either there is a very big step I'm missing or I've drawn something horribly wrong.

The first thing to determine is which angle is meant. Is the angle measured from the bank of the river to the boat's velocity vector, or is it measured from a line perpendicular to the bank? After that it's a matter of drawing the diagram and labeling the appropriate sides with the given information.

 

[bajangal1]

Ok i think i was drawing it wrong. i drew it differently and used sin inverse (2/4) and got the right answer. thanks!