A ship is being pulled by two tugboats. The larger tugboat exerts a force 25% greater
than the smaller tugboat and at an angle of 20 degrees west of north.
In what direction should the smaller tugboat pull in order for the ship to head
north?
So far, I assume the smaller force is $x$, so the The larger tugboat exerts a force is $1.25x
\tan(20)=1.25 x/m$, so $m=1.25x/tan20$. also, $x/(1.25x/\tan20)=tan\theta$ which $theta$ is the direction should the smaller tugboat pull in order for the ship to head north. $\theta=\arctan(\tan(20/1.25))$, so am I right of the track?
[Math] A ship is being pulled by two tugboats problems
calculus
Best Answer
Let the magnitude of the larger force be $1.25$. So the smaller one has magnitude $1$.
The west component of the force exerted by the larger tug is $1.25 \sin(20^\circ)$. This must be balanced by the east component of the force exerted by the little tug, which is $\sin(\theta)$. I expect you can now find $\theta$.
Remark: The answer reached in the OP does not make physical sense, for it is clear that the little tug must head more than $20^\circ$ east of north to compensate for the extra power of the big tug.