[Mike isaac]

A boat soils 4km on a bearing 038degree and then 5km on a bearing of 067degree.(a)how far is the boat from its starting point? (b)calculate the bearing of the boat from its starting point?

[zenton]

Bearing from the point after 4km to the starting point is 180-038=142degree.
So if you draw the 4km line and 5km lines on a piece of paper, there are 3 angles around that point 4km from the starting point, with 142 and 67 degree.
Find the last angle which is 360-142-67=151 degree.

a)
Using the cosine rule,
the distance=√(4x4+5x5-2x4x5xcos151)
=√75.98479
=8.71693
=8.72 (3s.f.)

b)
Using Sin rule,
sin151 / 8.71693=sinX / 5
sinX=0.27809
X=016.14624 degrees (5d.p.)

bearing of the boat from its starting point=016.14624+038
=054.1 degree

:D
Good Luck!