+25 A yacht sails on a bearing of 065 for 4km and then sails 8km along a bearing of 195. Find the distance and bearing of the yacht from its starting position
+129849 Using the Law of Cosines.......we can determine the distance, d, between his starting point and his ending point........so we have
d^2 = 4^2 + 8^2 - 2(4*8)cos(140)
d^2 = about 129.03 mi
d = √129.03 = about 11.359 miles
And we can use the Law of Sines to find the included angle, A, between the first leg of the journey and his last leg of the journey.........so we have
sin140/ 11.359 = sinA/8
8*sin140/11.359 = sinA
So
A = arcsin [ 8*sin140/11.359] = about 26.92°
Subtract 25 from this = 1.92°
Add this angle to the bearing of 270 = 271.92
So the yacht is about 11.359 miles from its starting position
And the bearing of the yacht to its starting position is 271.92°
