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?

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*}