I must assume you are familiar with vectors.
A boat heads in the direction N 40░ W at a speed of 24 knots.
The current runs at 6 knots in the direction N 25░ E.
Find the resultant speed and direction of the boat.
E 6Ěsin25░ C
+ - - - - - *
6Ěcos25░ : / 6
: / 24Ěsin24░
B * - - - - - - + D
\ : 24Ěcos24░
24 \ :
The boat is moving from point A to point B.
. . Its horizontal component is: DB = -24Ěsin24░
. . Its vertical component is: AD = 24Ěcos24░
The current is moving from point B to point C.
. . Its horizontal component is: EC = 6Ěsin25░
. . Its vertical component is: BE = 6Ěcos25░
The resultant vector is AC.
We must determine its magnitude and direction.
The horizontal component of AC is: .-24Ěsin24░ + 6Ěsin25░ .≈ .-7.226
The vertical component of AC is: .24Ěcos24░ + 6Ěcos25░ .≈ .27.363
. . . . . . . . . . . . . . . . . . . . . ________________
The magnitude is: .|AC| .= .√(-7.226)▓ + 27.363▓ .= .28.30103965
. . Therefore, the speed of the boat is about 28.3 knots.
The direction angle is given by: .tanθ .= .7.226/27.363 . → . θ .= .14.79292136░
. . Therefore, the direction is about: .N 14.8░ W