trig
posted by janice on .
A barge is pulled by two tugboats. The first tugboat is traveling at a speed of 16 knots with heading 135°, and the second tugboat is traveling at a speed of 15 knots with heading 195°. Find the resulting speed and direction of the barge. (Round your answers to the nearest whole number.)

V = 16Knots @ 135o+15Knots @ 195o.
X = 16*cos135 + 15*cos195 = 25.80 Knots
Y = 16*sin135 + 15*sin195 = 7.43 Knots.
tanA = Y/X = 7.43/25.80 = 0.28798
Ar = 16.07o = Reference angle.
A = 16.07 + 180 = 164o = Direction.
V = X/cosA = 25.80/cos164 = 27 Knots.