Expert: Paul Klarreich - 3/7/2008

Question
A person who can row 2.6 mph in still water wants to row due east across a river. The river is flowing from the north at a rate of 0.8 mph. Determine the heading of the boat that will be required for it to travel due east across the river.
Now this is what I have so far:  AC=2.6   CB=.8   AC=East  angle CAB=theta
then I have sin(theta)=.8/2.6
sin(theta)=.3077
Alas this is where my trigonometric mind comes to a halt.  Please show me the steps from here, or even back up if I messed something up. thanks much

Answer
Questioner:   Richard
Category:  Advanced Math
Private:  No
 
Subject:  Vectors

....................
Hi, Richard,

Question:  A person who can row 2.6 mph in still water

>> This guy must be an Olympic champion, but let it pass.

>> Draw an arrow going sort of up-ish and to the right.  Call it RA = 2.6.

wants to row due east across a river.

>> Draw an arrow going RIGHT. Length unknown.  Call it R-something. It will become RB.

The river is flowing from the north at a rate of 0.8 mph.

>> Draw an arrow going DOWN FROM A meeting R-something at B. Length = 0.8.  
This is AB.

Determine the heading of the boat that will be required for it to travel due east across the river.
Now this is what I have so far:  AC=2.6   CB=.8   AC=East  angle CAB=theta

>> Okay. I have RA = 2.6, AB = 0.8 and points East, angle ARB = theta.

then I have sin(theta)=.8/2.6
sin(theta)=.3077

>> Yes, yes, with yours my figures do agree.

Alas this is where my trigonometric mind comes to a halt.  Please show me the steps from here, or even back up if I messed something up. thanks much

>> Take out (well, open it up) your Windows calculator, put it into scientific view, then do:

0.8
/
2.6
=
Inv
Sin
and you get your answer, in degrees or radians, depending on which 'trig' button is active.

I get about 17.9 degrees.  I think you are supposed to make that 72.1 degrees East-North-East or something -- you better ask someone else about that.