Find the magnitude of the velocity of the canoe relative to the river?

for the velocity of the canoe relative to the Earth, it says southeast..u need an angle for that before u can figure out the velocity of the canoe relative to the river.

Draw a triangle ABC in which:
AB = 0.34 SE, representing the velocity of the canoe relative to earth;
AC = 0.57 E, representing the velocity of the river relative to earth.
CB is the vector which added to AC gives AB. That is the velocity of the boat relative to the river.

Noting that angle BAC = 45deg, and using the cosine rule:
CB = sqrt[ 0.34^2 + 0.57^2 - 2 * 0.34 * 0.57 cos(45) ]
= 0.408m/sec.

Using the sine rule:
sin(ACB) = 0.34 * sin(45) / 0.408
Angle ACB = 36.11deg.
As AC points E, this direction is:
90 - 36.11
= S 53.89 deg. W.

**source-straight from yahoo