a yacht is moving at 10km/h in a south easterly direction and encounters a 3km/h current from the north. find the actual speed and direction of the yacht

Answer 1

I made a sketch and it looks like a simple cosine law problem
d^2 = 10^2 + 3^2 - 2(10)(3)cos135
= 151.426...
d = 12.3 km/hr

then to find the small acute angle Ø
sinØ/3 = sin 135°/12.3..
sinØ = .1723..
Ø = 9.927°

direction is S (45-9.927..)° E
= S 35° E to the nearest degree