Q:

Find the resulting speed and direction. Trig Problem involving resultant and vectors.

A barge is pulled by two tugboats. The first tugboat is traveling at a speed of 15 knots with heading 130°, and the second tugboat is traveling at a speed of 11 knots with heading 190°. Find the resulting speed and direction of the barge. (Round your answers to the nearest whole number.)

$$
|v+w|^2=15^2+11^2-2(15)(11)cos120
$$
$$
|v+w|^2=511
$$
$$
|v+w| = 22.60530911 = 23
$$
$$
sinB= 11sin(12)/22.60530911
$$
$$
SinB=0.421417792
$$
$$
B=25
$$
$$
130+25=155
$$
I'm getting a speed of $23$ knots and a direction of $155°$.  Is this correct?

A:

Your answer is correct.
\begin{align*}
x &= 15 \cos 130^\circ  + 11 \cos 190^\circ \approx -20.4746994 \text{ knots} \\
y &= 15 \sin 130^\circ  + 11 \sin 190^\circ \approx 9.5805366 \text{ knots} \\
r &= \sqrt{x^2 + y^2} \approx 22.6 \text{ knots} \\
\theta &= 180^\circ + \arctan (y \; / \; x) \approx 154.9^\circ
\end{align*}

