A yacht sets sail from a harbour and sails on a bearing of 065T for 3.4km. it then turns and sails on a bearing of 127T for another 5km. On what bearing (to the nearest minute) should the yacht sail if it was to travel directly back to the harbour?

Answer 1

The yacht should take a bearing of the harbour, and then sail on that heading.

Not sure what 065T means, but I assume it's 65° clockwise from True North. If so, then the heading back to the harbour is found via

Label the diagram as follows:

H = harbour
P = point of turning
Q = final location
If the sides opposite these angles of triangle HPQ are h,p,q respectively, then

p^2 = 3.4^2 + 5^2 - 2*3.4*5*cos(138°) = 61.83
p = 7.86

Then to find angle Q,

sinQ/3.4 = sin138°/7.86
Q = 16.82° ≈ 17°

So the bearing of the harbour from Q is 360-(63+17) = 280°

Answer 2

Thanks, i got roughly the same answer, 282.